MATH 225N Statistics Final EXAM – Chamberlain College of Nursing MATH 225N Statistics Final EXAM

MATH 225N Statistics Final EXAM – Chamberlain College of Nursing MATH 225N Statistics Final EXAM 1/1 POINTS A fitness center claims that the mean amount of time that a person spends at the gym per visit is 33 minutes. Identify the null hypothesis, H0, and the alternative hypothesis, Ha, in terms of the parameter μ. That is correct! H0: μ≠33; Ha: μ=33 H0: μ=33; Ha: μ≠33 H0: μ≥33; Ha: μ<33 H0: μ≤33; Ha: μ>33 Answer Explanation Correct answer: H0: μ=33; Ha: μ≠33 Let the parameter μ be used to represent the mean. The null hypothesis is always stated with some form of equality: equal (=), greater than or equal to (≥), or less than or equal to (≤). Therefore, in this case, the null hypothesis H0 is μ=33. The alternative hypothesis is contradictory to the null hypothesis, so Ha is μ≠33. QUESTION 2 1/1 POINTS The answer choices below represent different hypothesis tests. Which of the choices are right-tailed tests? Select all correct answers. That is correct! • H0:X≥17.1, Ha:X<17.1 • • H0:X=14.4, Ha:X≠14.4 • • H0:X≤3.8, Ha:X>3.8 • • H0:X≤7.4, Ha:X>7.4 • • H0:X=3.3, Ha:X≠3.3 • Answer Explanation Correct answer: H0:X≤3.8, Ha:X>3.8 H0:X≤7.4, Ha:X>7.4 Remember the forms of the hypothesis tests. • Right-tailed: H0:X≤X0, Ha:X>X0. • Left-tailed: H0:X≥X0, Ha:X<X0. • Two-tailed: H0:X=X0, Ha:X≠X0. So in this case, the right-tailed tests are: • H0:X≤7.4, Ha:X>7.4 • H0:X≤3.8, Ha:X>3.8 QUESTION 3 0/1 POINTS Find the Type II error given that the null hypothesis, H0, is: a building inspector claims that no more than 15% of structures in the county were built without permits. That's not right. The building inspector thinks that no more than 15% of the structures in the county were built without permits when, in fact, no more than 15% of the structures really were built without permits. The building inspector thinks that more than 15% of the structures in the county were built without permits when, in fact, more than 15% of the structures really were built without permits. The building inspector thinks that more than 15% of the structures in the county were built without permits when, in fact, at most 15% of the structures were built without permits. The building inspector thinks that no more than 15% of the structures in the county were built without permits when, in fact, more than 15% of the structures were built without permits. Answer Explanation Correct answer: The building inspector thinks that no more than 15% of the structures in the county were built without permits when, in fact, more than 15% of the structures were built without permits. A Type II error is the decision not to reject the null hypothesis when, in fact, it is false. In this case, the Type II error is when the building inspector thinks that no more than 15% of the structures were built without permits when, in fact, more than 15% of the structures were built without permits. Your answer: The building inspector thinks that more than 15% of the structures in the county were built without permits when, in fact, at most 15% of the structures were built without permits. Content attribution- Opens a dialog QUESTION 4 1/1 POINTS Suppose a chef claims that her meatball weight is less than 4 ounces, on average. Several of her customers do not believe her, so the chef decides to do a hypothesis test, at a 10% significance level, to persuade them. She cooks 14 meatballs. The mean weight of the sample meatballs is 3.7 ounces. The chef knows from experience that the standard deviation for her meatball weight is 0.5 ounces. • H0: μ≥4; Ha: μ<4 • α=0.1 (significance level) What is the test statistic (z-score) of this one-mean hypothesis test, rounded to two decimal places? That is correct! $$Test statistic = −2.24 Answer Explanation Correct answers: • $text{Test statistic = }-2.24$Test statistic = −2.24​The hypotheses were chosen, and the significance level was decided on, so the next step in hypothesis testing is to compute the test statistic. In this scenario, the sample mean weight, x¯=3.7. The sample the chef uses is 14 meatballs, so n=14. She knows the standard deviation of the meatballs, σ=0.5. Lastly, the chef is comparing the population mean weight to 4 ounces. So, this value (found in the null and alternative hypotheses) is μ0. Now we will substitute the values into the formula to compute the test statistic: z0=x¯−μ0σn√=3.7−40.514√≈−0.30.134≈−2.24 So, the test statistic for this hypothesis test is z0=−2.24. QUESTION 5 1/1 POINTS What is the p-value of a right-tailed one-mean hypothesis test, with a test statistic of z0=1.74? (Do not round your answer; compute your answer using a value from the table below.) z1.51.61.71.81.90.000.9330.9450.9550.9640.9710.010.9340.9460.9560.9650.9720.020.9360.9470.9570.9660.9730.030.9370.9480.9580.9660.9730.040.9380.9490.9590.9670.9740.050.9390.9510.9600.9680.9740.060.9410.9520.9610.9690.9750.070.9420.9530.9620.9690.9760.080.9430.9540.9620.9700.9760.090.9440.9540.9630.9710.977 That is correct! $$0.041 Answer Explanation Correct answers: • $0.041$0.041​The p-value is the probability of an observed value of z=1.74 or greater if the null hypothesis is true, because this hypothesis test is right-tailed. This probability is equal to the area under the Standard Normal curve to the right of z=1.74. A standard normal curve with two points labeled on the horizontal axis. The mean is labeled at 0.00 and an observed value of 1.74 is labeled. The area under the curve and to the right of the observed value is shaded. Using the Standard Normal Table, we can see that the p-value is equal to 0.959, which is the area to the left of z=1.74. (Standard Normal Tables give areas to the left.) So, the p-value we're looking for is p=1−0.959=0.041. QUESTION 6 1/1 POINTS Kenneth, a competitor in cup stacking, claims that his average stacking time is 8.2 seconds. During a practice session, Kenneth has a sample stacking time mean of 7.8 seconds based on 11 trials. At the 4% significance level, does the data provide sufficient evidence to conclude that Kenneth's mean stacking time is less than 8.2 seconds? Accept or reject the hypothesis given the sample data below. • H0:μ=8.2 seconds; Ha:μ<8.2 seconds • α=0.04 (significance level) • z0=−1.75 • p=0.0401 That is correct! Do not reject the null hypothesis because the p-value 0.0401 is greater than the significance level α=0.04. Reject the null hypothesis because the p-value 0.0401 is greater than the significance level α=0.04. Reject the null hypothesis because the value of z is negative. Reject the null hypothesis because |−1.75|>0.04. Do not reject the null hypothesis because |−1.75|>0.04. Answer Explanation Correct answer: Do not reject the null hypothesis because the p-value 0.0401 is greater than the significance level α=0.04. In making the decision to reject or not reject H0, if α>p-value, reject H0 because the results of the sample data are significant. There is sufficient evidence to conclude that H0 is an incorrect belief and that the alternative hypothesis, Ha, may be correct. If α≤p-value, do not reject H0. The results of the sample data are not significant, so there is not sufficient evidence to conclude that the alternative hypothesis, Ha, may be correct. In this case, α=0.04 is less than or equal to p=0.0401, so the decision is to not reject the null hypothesis. QUESTION 7 1/1 POINTS A recent study suggested that 81% of senior citizens take at least one prescription medication. Amelia is a nurse at a large hospital who would like to know whether the percentage is the same for senior citizen patients who go to her hospital. She randomly selects 59 senior citizens patients who were treated at the hospital and finds that 49 of them take at least one prescription medication. What are the null and alternative hypotheses for this hypothesis test? That is correct! {H0:p=0.81Ha:p>0.81 {H0:p≠0.81Ha:p=0.81 {H0:p=0.81Ha:p<0.81 {H0:p=0.81Ha:p≠0.81 Answer Explanation Correct answer: {H0:p=0.81Ha:p≠0.81 First verify whether all of the conditions have been met. Let p be the population proportion for the senior citizen patients treated at Amelia's hospital who take at least one prescription medication. 1. Since there are two independent outcomes for each trial, the proportion follows a binomial model. 2. The question states that the sample was collected randomly. 3. The expected number of successes, np=47.79, and the expected number of failures, nq=n(1−p)=11.21, are both greater than or equal to 5. Since Amelia is testing whether the proportion is the same, the null hypothesis is that p is equal to 0.81 and the alternative hypothesis is that p is not equal to 0.81. The null and alternative hypotheses are shown below. {H0:p=0.81Ha:p≠0.81 QUESTION 8 1/1 POINTS A researcher claims that the proportion of cars with manual transmission is less than 10%. To test this claim, a survey checked 1000 randomly selected cars. Of those cars, 95 had a manual transmission. The following is the setup for the hypothesis test: {H0:p=0.10Ha:p<0.10 Find the test statistic for this hypothesis test for a proportion. Round your answer to 2 decimal places. That is correct! $$Test_Statistic=−0.53 Answer Explanation Correct answers: • $text{Test_Statistic}=-0.53$Test_Statistic=−0.53​The proportion of successes is p^==0.095. The test statistic is calculated as follows: z=p^−p0p0⋅(1−p0)n−−−−−−√ z=0.095−0.100.10⋅(1−0.10)1000−−−−−−−−√ z≈−0.53 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - QUESTION 39 1/1 POINTS The population standard deviation for the heights of dogs, in inches, in a city is 3.7 inches. If we want to be 95% confident that the sample mean is within 2 inches of the true population mean, what is the minimum sample size that can be taken? z0.101.282z0.051.645z0.0251.960z0.012.326z0.0052.576 Use the table above for the z-score, and be sure to round up to the nearest integer. That is correct! $$14 dog heights Answer Explanation Correct answers: • $14text{ dog heights}$14 dog heights​The formula for sample size is n=z2σ2EBM2. In this formula, z=zα2=z0.025=1.96, because the confidence level is 95%. From the problem, we know that σ=3.7 and EBM=2. Therefore, n=z2σ2EBM2=(1.96)2(3.7)222≈13.15. Use n=14 to ensure that the sample size is large enough. Also, the sample size formula shown above is sometimes written using an alternate format of n=(zσE)2. In this formula, E is used to denote margin of error and the entire parentheses is raised to the exponent 2. Therefore, the margin of error for the mean can be denoted by "EBM" or by "E". Either formula for the sample size can be used and these formulas are considered as equivalent. QUESTION 40 · 0/1 POINTS Which of the following frequency tables show a skewed data set? Select all answers that apply. That's not right. • Value Frequency • • Value Frequency • • Value Frequency 15 20 3 • • Value Frequency 2 • Answer Explanation Correct answer: Value Frequency 15 20 3 Value Frequency 2 Remember that data are left skewed if there is a main concentration of large values with several much smaller values. Similarly, right skewed data have a main concentration of small values with several much larger values. We can see that the following is left skewed because of the concentration of large values with many smaller values: Value Frequency 15 20 3 And the following is right skewed because of its concentration of small values with many larger values: Value Frequency 2 The other frequency tables are more balanced and symmetrical. Your answer: Value Frequency The data in this table is roughly symmetrical about 10. Value Frequency 15 20 3 Correct! QUESTION 41 1/1 POINTS A poll was conducted during the final game of the basketball season to determine whether fans wanted to see the defending champions win the game or the challenging team win the game. From the poll, 216 of the 374 residents sampled from urban areas want the defending champions to win the game. In more rural areas, 304 of the 466 residents polled want the defending champions to win the game. Assuming location has nothing to do with team preference, the probability that the data gathered was the result of chance is calculated to be 0.03. What is the correct interpretation of this calculation? That is correct! More people from rural areas want the defending champions to win the game. Exactly 216 out of every 374 urban residents want the defending champions to win the game. The results are statistically significant at the 0.05 level of significance in showing that the proportion of people in rural areas who want the defending champions to win the game is different than the proportion of people in urban areas. The data is not statistically significant at the 0.05 level of significance in showing that the proportion of people in rural areas who want the defending champions to win the game is different than the proportion of people in urban areas. Answer Explanation Correct answer: The results are statistically significant at the 0.05 level of significance in showing that the proportion of people in rural areas who want the defending champions to win the game is different than the proportion of people in urban areas. The probability value calculated is 0.03. This is less than 0.05, so we conclude that the data are statistically significant in showing that the proportion of people in rural areas who want the defending champions to win the game is different than the proportion of people in urban areas. QUESTION 42 1/1 POINTS In a psychological study aimed at testing a drug that reduces anxiety, the researcher grouped the participants into 2 groups and gave the anxiety-reduction pill to one group and an inert pill to another group. Which group receives the placebo? That is correct! the group that received the anxiety-reduction pill the psychological study all the people in the study the group that received the inert pill Answer Explanation Correct answer: the group that received the inert pill When the experimental units are people, applying treatments that should be inert can actually have effects. So the group that received the inert pill received the placebo. QUESTION 43 1/1 POINTS Which of the following results in the null hypothesis μ≥38 and alternative hypothesis μ<38? That is correct! A fitness center claims that the mean amount of time that a person spends at the gym per visit is at most 38 minutes. A fitness center claims that the mean amount of time that a person spends at the gym per visit is fewer than 38 minutes. A fitness center claims that the mean amount of time that a person spends at the gym per visit is 38 minutes. A fitness center claims that the mean amount of time that a person spends at the gym per visit is more than 38 minutes. Answer Explanation Correct answer: A fitness center claims that the mean amount of time that a person spends at the gym per visit is fewer than 38 minutes. Consider each of the options. The scenario in option B has the null hypothesis μ≥38 based on the words "fewer than" and the fact that the null hypothesis is always stated with some form of equality. QUESTION 44 1/1 POINTS True or False: The more shoes a manufacturer makes, the more shoes they sell. That is correct! True False Answer Explanation Correct answer: False In supply and demand, a company doesn't make a product hoping that someone will buy them, they have a Demand first for their product and then, they produce more of that given product. QUESTION 45 1/1 POINTS Fill in the following contingency table and find the number of students who both do not play sports AND do not play an instrument. StudentsplaysportsdonotplaysportsTotalplayaninstrument33donotplayaninstrument69Total6267 That is correct! $$34 Answer Explanation Correct answers: • $34$34​By using the known totals along the rows and columns you can fill in the rest of the contingency table. For example, looking at the second row in the table, we know that 33 added to the unknown number in the middle is 67, so that unknown number is 34. Continuing in this way, we can fill in the entire table: StudentsplaysportsdonotplaysportsTotalplayaninstrumentdonotplayaninstrumentTotal From this, we can see that the number of students who both do not play sports and do not play an instrument is 34. FEEDBACK • • • • Content attribution- Opens a dialog QUESTION 45 1/1 POINTS Fill in the following contingency table and find the number of students who both do not play sports AND do not play an instrument. StudentsplaysportsdonotplaysportsTotalplayaninstrument33donotplayaninstrument69Total6267 That is correct! $$34 Answer Explanation Correct answers: • $34$34​By using the known totals along the rows and columns you can fill in the rest of the contingency table. For example, looking at the second row in the table, we know that 33 added to the unknown number in the middle is 67, so that unknown number is 34. Continuing in this way, we can fill in the entire table: StudentsplaysportsdonotplaysportsTotalplayaninstrumentdonotplayaninstrumentTotal From this, we can see that the number of students who both do not play sports and do not play an instrument is 34. QUESTION 46 1/1 POINTS The answer choices below represent different hypothesis tests. Which of the choices are left-tailed tests? Select all correct answers. That is correct! • H0:X=17.3, Ha:X≠17.3 • • H0:X≥19.7, Ha:X<19.7 • • H0:X≥11.2, Ha:X<11.2 • • H0:X=13.2, Ha:X≠13.2 • • H0:X=17.8, Ha:X≠17.8 • Answer Explanation Correct answer: H0:X≥19.7, Ha:X<19.7 H0:X≥11.2, Ha:X<11.2 Remember the forms of the hypothesis tests. • Right-tailed: H0:X≤X0, Ha:X>X0. • Left-tailed: H0:X≥X0, Ha:X<X0. • Two-tailed: H0:X=X0, Ha:X≠X0. So in this case, the left-tailed tests are: • H0:X≥11.2, Ha:X<11.2 • H0:X≥19.7, Ha:X<19.7 QUESTION 47 1/1 POINTS Assume the null hypothesis, H0, is: Jacob earns enough money to afford a luxury apartment. Find the Type I error in this scenario. That is correct! Jacob thinks he does not earn enough money to afford the luxury apartment when, in fact, he does. Jacob thinks he does not earn enough money to afford the luxury apartment when, in fact, he does not. Jacob thinks he earns enough money to afford the luxury apartment when, in fact, he does not. Jacob thinks he earns enough money to afford the luxury apartment when, in fact, he does. Answer Explanation Correct answer: Jacob thinks he does not earn enough money to afford the luxury apartment when, in fact, he does. A Type I error is the decision to reject the null hypothesis when it is true. In this case, the Type I error is when Jacob thinks he does not earn enough money when he really does. QUESTION 48 1/1 POINTS Given the plot of normal distributions A and B below, which of the following statements is true? Select all correct answers. A normal bell curve labeled Upper A and a normal elongated curve labeled Upper B are centered at the same point. Normal curve Upper B is narrower and above normal curve Upper A. That is correct! • A has the larger mean. • • B has the larger mean. • • The means of A and B are equal. • • A has the larger standard deviation. • • B has the larger standard deviation. • • The standard deviations of A and B are equal. • Answer Explanation Correct answer: The means of A and B are equal. A has the larger standard deviation. Remember that the mean of a normal distribution is the x-value of its central point (the top of the "hill"). Therefore, a distribution with a larger mean will be centered farther to the right than a distribution with a smaller mean.

Because A and B are centered at the same point, their means are equal.

Remember that the standard deviation tells how spread out the normal distribution is. So a high standard deviation means the graph will be short and spread out. A low standard deviation means the graph will be tall and skinny.

Because A is shorter and more spread out than B, we find that A has the larger standard deviation. QUESTION 49 1/1 POINTS Hugo averages 72 words per minute on a typing test with a standard deviation of 12 words per minute. Suppose Hugo's words per minute on a typing test are normally distributed. Let X= the number of words per minute on a typing test. Then, X∼N(72,12).

Suppose Hugo types 54 words per minute in a typing test on Wednesday. The z-score when x=54 is ________. This z-score tells you that x=54 is ________ standard deviations to the ________ (right/left) of the mean, ________.

Correctly fill in the blanks in the statement above. That is correct! Suppose Hugo types 54 words per minute in a typing test on Wednesday. The z-score when x=54 is −1.2. This z-score tells you that x=54 is 1.2 standard deviations to the left of the mean, 72. Suppose Hugo types 54 words per minute in a typing test on Wednesday. The z-score when x=54 is 1.2. This z-score tells you that x=54 is 1.2 standard deviations to the right of the mean, 72. Suppose Hugo types 54 words per minute in a typing test on Wednesday. The z-score when x=54 is 1.5. This z-score tells you that x=54 is 1.5 standard deviations to the right of the mean, 72. Suppose Hugo types 54 words per minute in a typing test on Wednesday. The z-score when x=54 is −1.5. This z-score tells you that x=54 is 1.5 standard deviations to the left of the mean, 72. Answer Explanation Correct answer: Suppose Hugo types 54 words per minute in a typing test on Wednesday. The z-score when x=54 is −1.5. This z-score tells you that x=54 is 1.5 standard deviations to the left of the mean, 72. The z-score can be found using the formula z=x−μσ=54−7212=−1812≈−1.5 A negative value of z means that that the value is below (or to the left of) the mean, which was given in the problem as μ=72 words per minute in a typing test. The z-score tells you how many standard deviations the value x is above (to the right of) or below (to the left of) the mean, μ. So, typing 54 words per minute is 1.5 standard deviations away from the mean. QUESTION 50 1/1 POINTS The following frequency table summarizes a set of data. What is the five-number summary? Value Frequency That is correct! Min Q1 Median Q3 Max Min Q1 Median Q3 Max Min Q1 Median Q3 Max Min Q1 Median Q3 Max Min Q1 Median Q3 Max Answer Explanation Correct answer: Min Q1 Median Q3 Max We can immediately see that the minimum value is 1 and the maximum value is 22.

If we add up the frequencies in the table, we see that there are 19 total values in the data set. Therefore, the median value is the one where there are 9 values below it and 9 values above it. By adding up frequencies, we see that this happens at the value 10, so that is the median.

Now, looking at the lower half of the data, there are 9 values there, and so the median value of that half of the data is 2. This is the first quartile. Similarly, the third quartile is the median of the upper half of the data, which is 12.
1, 1, 1, 1, 2, 2, 7, 8, 9, 10, 10, 10, 10, 12, 12, 12, 16, 20, 22
So, the five-number summary is Min Q1 Median Q3 Max