MATH 225 Week 5 - 8 Final Exam Question and Answers

QUESTION 1·1 POINT 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. Select the correct answer below: H0: μ≠33; Ha: μ=33 H0: μ=33; Ha: μ≠33 H0: μ≥33; Ha: μ33 H0: μ≤33; Ha: μ33 QUESTION 2·1 POINT The answer choices below represent different hypothesis tests. Which of the choices are righttailed tests? Select all correct answers. Select all that apply: • H0:X≥17.1, Ha:X17.1 • • • H0:X≤3.8, Ha:X3.8 • • H0:X≤7.4, Ha:X7.4 • • H0:X=3.3, Ha:X≠3.3 • H0:X=14.4, Ha:X≠14.4 • QUESTION 3·1 POINT 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: μ4 • α=0.1 (significance level) What is the test statistic (z-score) of this one-mean hypothesis test, rounded to two decimal places? Provide your answer below: $$Test statistic = QUESTION 4·1 POINT 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.) The p-value is equal to the area under the Standard Normal curve to the right of z=1.74. To the left, the p-value = 0.959. Therefore, the p-value to the right is 1-0.959 = 0.041 Test statistic =-2.24 QUESTION 5·1 POINT 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:μ8.2 seconds • α=0.04 (significance level) • z0=−1.75 • p=0.0401 Select the correct answer below: 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. QUESTION 6·1 POINT 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? Select the correct answer below: {H0:p=0.81Ha:p0.81 {H0:p≠0.81Ha:p=0.81 {H0:p=0.81Ha:p0.81 {H0:p=0.81Ha:p≠0.81 QUESTION 7·1 POINT 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:p0.10 Find the test statistic for this hypothesis test for a proportion. Round your answer to 2 decimal places. Test statistic, z = 0.095-0.1(0.1)(1-0.1)1000 = -0.53 Provide your answer below: $$Test_Statistic= QUESTION 8·1 POINT A medical researcher claims that the proportion of people taking a certain medication that develop serious side effects is 12%. To test this claim, a random sample of 900 people taking the medication is taken and it is determined that 93 people have experienced serious side effects. The following is the setup for this hypothesis test: H0:p = 0.12 Ha:p ≠ 0.12 Find the p-value for this hypothesis test for a proportion and round your answer to 3 decimal places. z=0.1033-0.120*12(1-0.12)900 =-1.54 The corresponding area will be 2(0.062) = 0.124 The following table can be utilized which provides areas under the Standard Normal Curve: z 0.00 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 -1.8 0.036 0.035 0.034 0.034 0.033 0.032 0.031 0.031 0.030 0.029 -1.7 0.045 0.044 0.043 0.042 0.041 0.040 0.039 0.038 0.038 0.037 -1.6 0.055 0.054 0.053 0.052 0.051 0.049 0.048 0.047 0.046 0.046 -1.5 0.067 0.066 0.064 0.063 0.062 0.061 0.059 0.058 0.057 0.056 -1.4 0.081 0.079 0.078 0.076 0.075 0.074 0.072 0.071 0.069 0.068 z =-0.53 Provide your answer below: $$P-value= QUESTION 9·1 POINT An economist claims that the proportion of people who plan to purchase a fully electric vehicle as their next car is greater than 65%. To test this claim, a random sample of 750 people are asked if they plan to purchase a fully electric vehicle as their next car Of these 750 people, 513 indicate that they do plan to purchase an electric vehicle. The following is the setup for this hypothesis test: H0:p=0.65 Ha:p0.65 In this example, the p-value was determined to be 0.026. Come to a conclusion and interpret the results for this hypothesis test for a proportion (use a significance level of 5%.) Select the correct answer below: The decision is to reject the Null Hypothesis. The conclusion is that there is enough evidence to support the claim. P-value =0.124 The decision is to fail to reject the Null Hypothesis. The conclusion is that there is not enough evidence to support the claim. QUESTION 10·1 POINT Becky's statistics teacher was teaching the class how to perform the z-test for a proportion. Becky was bored because she had already mastered the test, so she decided to see if the coin she had in her pocket would come up heads or tails in a truly random fashion when flipped. She discretely flipped the coin 30 times and got heads 18 times. Becky conducts a one-proportion hypothesis test at the 5% significance level, to test whether the true proportion of heads is different from 50%. Which answer choice shows the correct null and alternative hypotheses for this test? Select the correct answer below: H0:p=0.6; Ha:p0.6, which is a right-tailed test. H0:p=0.5; Ha:p0.5, which is a left-tailed test. H0:p=0.6; Ha:p≠0.6, which is a two-tailed test. H0:p=0.5; Ha:p≠0.5, which is a two-tailed test.