BUAL 2650 Final Exam

Suppose that a random variable x has a uniform distribution with c = 2 and d =8. Find P(3 = x = 5) - -.333 Find the area under the normal curve when P(Z -2) - -.9772 Find the area under the normal curve between P(1 z 2) - -.1359 In a manufacturing process, we are interested in measuring the average length of a certain type of bolt. Past data indicate that the standard deviation is .25 inches. How many manufactured bolts should be sampled in order to make us 95 percent confident that the sample mean bolt length is within .02 inches of the true mean bolt length? - 601 Rejecting a true null hypothesis is called a ________ error. - -Type 1 A recent study conducted by the state government attempts to determine whether the voting public supports a further increase in cigarette taxes. The opinion poll recently sampled 1,500 voting-age citizens. 1,020 of the sampled citizens were in favor of an increase in cigarette taxes. The state government would like to decide if there is enough evidence to establish whether the proportion of citizens supporting an increase in cigarette taxes is significantly greater than .66. Identify the null hypothesis. - -p ≤ .66 In testing H0: μ= 23; versus HA: μ 23 using the critical value rule, when x¯ = 26, s = 6, and n = 20, what is the value of the test statistic? Assume that the population from which the sample is selected is normally distributed. - -2.24 In a manufacturing process, a random sample of 36 manufactured bolts has a mean length of 3 inches with a standard deviation of .3 inches. What is the 99 percent confidence interval for the true mean length of the manufactured bolt? - -2.228 to 3.772 A confidence interval for the population mean is an interval constructed around the ________. - -sample mean When the population is normally distributed, population standard deviation σ is unknown, and the sample size is n = 15, the confidence interval for the population mean μ is based on the z (normal) distribution. - -the t distribution The exact spread of the t distribution depends on the ________. - -number of degrees of freedom ______ says that if the sample size is sufficiently large, then the sample means are approximately normally distributed. - -The Central Limit Theorem BUAL 2650 BUAL 2650 The mean of a standard normal distribution is always equal to ________. - -0 ________ values of the standard deviation result in a normal curve that is wider and flatter. - -larger The area under the curve of a valid continuous probability distribution must ________. - -equal 1 A continuous probability distribution having a rectangular shape, where the probability is evenly distributed over an interval of numbers is a(n) ________ distribution - -uniform The specific shape of each normal distribution is determined by its ________ and ________. - -mean, standard deviation If the random variable x is normally distributed, ______ percent of all possible observed values of x will be within three standard deviations of the mean - -99.73 Which of the following statements is not a property of the normal probability distribution? - -95.44 percent of all possible observed values of the random variable x are within plus or minus three standard deviations of the population mean. The normal approximation of the binomial distribution is appropriate when - -np ≥ 5 and n(1 − p) ≥ 5. It is appropriate to use the uniform distribution to describe a continuous random variable x when - -relative frequencies of all possible values of x are about the same. The ________ is a graphic that is used to visually check whether data come from a normal population. - -normal probability plot The fill weight of a certain brand of adult cereal is normally distributed with a mean of 910 grams and a standard deviation of 5 grams. We calculated the value of z for a specific box of this brand of cereal, and the z value was negative. This negative z value indicates that. - -the fill weight is less than 910 grams. The z value tells us the number of ________ that a value of x is from the mean - standard deviations Packages of sugar bags for Sweeter Sugar Inc. have an average weight of 16 ounces and a standard deviation of .2 ounces. The weights of the sugar packages are normally distributed. What is the probability that 16 randomly selected packages will have a weight in excess of 16.075 ounces? - -.0668 As the standard deviation (σ) decreases, the width of the confidence interval ________. - -increases BUAL 2650 BUAL 2650 For a one-tailed test, the critical value: - -helps determine if the test statistic falls in the rejection region or not. What is the confidence coefficient when alpha value is .10? - -90% Reject H0 (Null Hypothesis) if - -p-value ∝ (alpha) The value of (1 - alpha) is called: - -confidence coefficient What is Null and alternate Hypothesis from this output? - -H0: mu = 330 H1: mu 330 What is the level of significance or alpha value from the output? - -0.05 What is the t (test statistic) value from the output? - --1.02 1. What are the degrees of freedom from the output? - -99 What is the p-value from the output? - -309 What is your conclusion from the output? - -Do not reject Ho or Fail to reject Ho Find P(-2 Z 2) - -.9544 Suppose that we will randomly select a sample of 64 measurements from a population having a mean equal to 20 and a standard deviation equal to 4. Find the mean and the standard deviation of the sampling distribution of the sample mean (x bar) - -sample mean = 20 , sample standard deviation = 0.5 Suppose we conduct a poll to estimate the proportion of voters who favor a major presidential candidate. Assuming that 50% of the electorate could be in favor of the candidate, determine the sample size needed so we are 95% confident that p-hat is within a margin of error of .01 of p. - -9604 A manufacturer wishes to determine if the average profit from the sale of his product exceeds $6,710. Which of the following is the appropriate hypothesis test? - -H0: population mean profit from sale ≤ $6,710 vs. H1: population mean profit from sale $6,710 In testing for the equality of means from two independent populations, if the hypothesis of equal population means is rejected at α = .01, it w