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Unformatted text preview: IET 2227 Prof. Greg Wiles SAMPLE EXAM 3 Name___________________________________ IMPORTANT:
• Do your own work
• Read instructions carefully
• Clearly indicate your answers
• You may use calculators for any part you wish
• Use your time wisely By my signature below, I certify that I have neither given nor received assistance on this exam.
__________________________________ MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Find the requested value. (6 points)
1) _______ 1) A researcher wishes to estimate the mean resting heart rate for longdistance runners. A random sample of 12 long‐distance runners yields the following heart rates, in beats per minute. Use the data to obtain a point estimate of the mean resting heart rate for all long distance runners. A) 69.6 beats per minute B) 67.8 beats per minute C) 66.2 beats per minute D) 64.6 beats per minute Find the requested confidence interval. (6 points)
2) A college statistics professor has office hours from 9:00 A.M. to 10:30 A.M. daily. A sample of waiting times to see the professor (in minutes) is 10, 12, 20, 15, 17, 10, 30, 28, 35, 28, 19, 27, 25, 22, 33, 37, 14, 21, 20, 23. find the 95.44% confidence interval for the Assuming population mean. A) 19.5 to 35.1 minutes B) 7.7 to 7.8 minutes C) 18.8 to 25.8 minutes D) 3.5 to 3.5 minutes Provide an appropriate response. (5 points)
3) Find the value of α that corresponds to a confidence level of 84%. A) 0.84 B) 16 C) 0.016 D) 0.16 2) _______ 3) _______ Provide an appropriate response. (5 points)
4) If the sample size is small (less than 15), under what conditions is it 4) _______ reasonable to use the z‐interval procedure to obtain a confidence interval for the population mean? A) When the variable under consideration is normally distributed or close to being so. B) No conditions, the original distribution does not matter. C) Only when there are outliers present. D) Never use the zinterval procedure for sample sizes less than 15. Find the specified tvalue. (5 points)
5) For a tcurve with df = 11, find t 0.10. 5) _______ A) 2.718 B) 1.363 C) 1.372 D) 1.280 Find the confidence interval specified. Assume that the population is normally distributed. (5 points)
6) A laboratory tested twelve chicken eggs and found that the mean 6) _______ amount of cholesterol was 186 milligrams with s = 19.0 milligrams. Construct a 95% confidence interval for the true mean cholesterol content of all such eggs. A) 173.8 to 198.2 milligrams B) 174.0 to 198.0 milligrams C) 176.1 to 195.9 milligrams D) 173.9 to 198.1 milligrams A hypothesis test is to be performed. Determine the null and alternative hypotheses. (5 points)
7) In the past, the mean running time for a certain type of flashlight battery 7) _______ has been 8.5 hours. The manufacturer has introduced a change in the production method and wants to perform a hypothesis test to determine whether the mean running time has changed as a result. A) B) : μ ≠ 8.5 hours : μ = 8.5 hours : μ = 8.5 hours C) : μ = 8.5 hours : μ ≠ 8.5 hours : μ > 8.5 hours D) : μ ≥ 8.5 hours : μ = 8.5 hours Classify the hypothesis test as twotailed, lefttailed, or righttailed. (5 points)
8) 8) _______ The recommended dietary allowance (RDA) of vitamin C for women is 75 milligrams per day. A hypothesis test is to be performed to decide whether adult women are, on average, getting less than the RDA of 75 milligrams per day. A) Twotailed B) Lefttailed C) Righttailed Write the word or phrase that best completes each statement or answers the question. (20 points)
9) A public bus company official claims that the mean waiting 9) _____________ time for bus number 14 during peak hours is 10 minutes. Karen took bus number 14 during peak hours on 18 randomly selected days. Her mean waiting time was 8 minutes. Do the data provide sufficient evidence to conclude that the mean waiting time differs from the 10 minutes claimed by the bus company? Assume that the population standard deviation of the waiting times is 2.2 minutes. Use the following steps to answer the question. a. State the null and alternative hypotheses. b. Discuss the logic of conducting the hypothesis test. c. Identify the distribution of the variable , that is, the sampling distribution of the mean for samples of size 18. d. Obtain a precise criterion for deciding whether to reject the null hypothesis in favor of the alternative hypothesis. Use the ʺ68.26ʺ part of the 68.2695.4499.74 rule. e. Apply the criterion in part (d) to the sample data and state your conclusion. MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. The graph portrays the decision criterion for a hypothesis test for a population mean. The null The curve is the normal curve for the test statistic under the assumption hypothesis is that the null hypothesis is true. Use the graph to solve the problem. (5points)
10) A graphical display of the decision criterion follows. 10) ______ Determine the rejection region. A) z ≥ 0.005 B) z ≥ 2.575 C) z ≤ 2.575 D) z = 2.575 For the given hypothesis test, explain the meaning of a Type I error, a Type II error, or a correct decision as specified. (5 points)
11) In the past, the mean running time for a certain type of flashlight battery 11) ______
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has been 8.9 hours. The manufacturer has introduced a change in the production method and wants to perform a hypothesis test to determine whether the mean running time has increased as a result. The hypotheses are: : μ = 8.9 hours : μ > 8.9 hours where μ is the mean running time of the new batteries . Explain the meaning of a Type I error. A) A Type I error would occur if, in fact, μ > 8.9 hours, but the results of the sampling lead to the conclusion that μ < 8.9 hours. B) A Type I error would occur if, in fact, μ > 8.9 hours, but the results of the sampling fail to lead to that conclusion. C) A Type I error would occur if, in fact, μ = 8.9 hours, but the results of the sampling do not lead to rejection of that fact. D) A Type I error would occur if, in fact, μ = 8.9 hours, but the results of the sampling lead to the conclusion that μ > 8.9 hours. A hypothesis test is to be performed for a population mean with null hypothesis : μ = . The test statistic used will be z = . Find the required critical value(s). (5 points) 12) A twotailed test with α = 0.05. 12) ______ A) ±1.96 B) ±2.575 C) ±1.645 D) ±1.764 Provide an appropriate response. (5 points)
13) 13) ______ A onesample ztest for a population mean is to be performed. Let denote the observed value of the test statistic, z. True or false, for a left‐
tailed test, the P‐value is the area under the standard normal curve to ? the left of A) True B) False A onesample ztest for a population mean is to be performed. The value obtained for the test statistic, is given: The nature of the test (right‐tailed, left‐tailed, or two‐tailed) is also specified. Determine the P‐value. (3 points) 14) A twotailed test: 14) ______ z = 1.31 A) 0.9049 B) 0.0951 C) 0.1902 D) 0.8098 A sample mean, sample standard deviation, and sample size are given. Use the onemean ttest to perform the required hypothesis test about the mean, μ, of the population from which the sample was drawn. Use the criticalvalue approach. (6 points)
15) 15) ______ n = 15, : μ = 32.6, : μ ≠ 32.6, α = 0.05. A) Test statistic: t = 5.21. Critical values: Do not reject There is not sufficient evidence to support the claim that the mean is different from 32.6. B) Test statistic: t = 5.21. Critical values: Reject There is sufficient evidence to support the claim that the mean is different from 32.6. C) Test statistic: t = 5.21. Critical values: Do not reject There is not sufficient evidence to support the claim that the mean is different from 32.6. D) Test statistic: t = 5.21. Critical values: Reject There is sufficient evidence to support the claim that the mean is different from 32.6. Provide an appropriate response. (6 points)
16) The Pvalue for a onemean ttest is estimated using a ttable as 0.05 < P < 0.10. Based on this information, for what significance levels can the null hypothesis be rejected? A) We can reject at any significance level smaller than 0.10. B) We can reject C) We can reject at any significance level 0.05 or larger. D) We can reject at any significance level 0.10 or larger. at any significance level smaller than 0.05. 16) ______ ...
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 Fall '09

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