# Statistics Question

Math 1342
HW 7 (Fall 2022)
1) The mean age of students at one CCQ statistic class is 24 years. Write the null and alternative
hypotheses.
2) A college claims that the mean time for students to earn an associate degree is at most 5 semesters.
Write the null and alternative hypotheses.
3) A car maker claims that one of its cars gets better than 20 Km per liter. Determine whether the
hypothesis test for this is left-tailed, right-tailed, or two-tailed.
4) Given Ho:
80% and Ha:
< 80%, determine whether the hypothesis test is left-tailed, right-tailed, or two-tailed. 5) The mean age of students at one college is 23 years. If a hypothesis test is performed, how should you interpret a decision that fails to reject the null hypothesis? A) There is not sufficient evidence to reject the claim µ = 23. B) There is sufficient evidence to reject the claim µ = 23. C) There is not sufficient evidence to support the claim µ = 23. D) There is sufficient evidence to support the claim µ = 23. 6) Suppose you want to test the claim that significance of < 65.4. Given a sample size of n = 35 and a level of = 0.05, when should you reject H o? A) Reject Ho if the standardized test statistic is less than -1.28. B) Reject Ho if the standardized test statistic is less than -1.645. C) Reject Ho if the standardized test is less than -1.96. D) Reject Ho if the standardized test statistic is less than -2.33. 7) The P-value for a hypothesis test is P = 0.034. Do you reject or fail to reject H 0 for level of significance = 0.05 8) Find the P-value for the hypothesis test with the standardized test statistic z. Decide whether to reject H 0 for the level of significance . Two-tailed test, z = -1.63, = 0.05 9) Find the P-value for the hypothesis test with the standardized test statistic z. Decide whether to reject Ho for the level of significance . Left-tailed test, z = -1.83, 10) Find the standardized test statistic t for a sample with n = 15, x = 7.2, s = 0.8, and Ho: = 0.05 = 0.05, if 6.9. 11) Find the critical value and rejection region for the type of z-test with level of significance . Left-tailed test, = 0.05 12) Find the critical value and rejection region for the type of t-test with level of significance sample size n. Right-tailed test, and = 0.1, n = 35 13) Find the critical value and rejection region for the type of z-test with level of significance . Two-tailed test, = 0.10 14) A fast food outlet claims that the mean waiting time in line is less than 3.8 minutes. A random sample of 60 customers has a mean of 3.7 minutes with a population standard deviation of 0.6 minute. If = 0.05, test the fast food outlet's claim. (Use the P-Value Method) a) State the hypotheses, and Identify the claim. b) Find the standardized test statistic z. c) Find the P-value. d) Decide whether to reject the null hypothesis or not. e) Interpret the decision in the context of the original claim. 15) A researcher claims that the mean age of residents in a small city is more than 21 years. A random sample of 37 residents has a mean age of 19 years with a standard deviation of 4 years. If is there enough evidence to reject the researcher's claim? = 0.01, a) Identify the claim and state the hypothesis b) Find the critical value and identify the rejection region. c) Find the standardized test statistic z. Sketch a graph. d) Decide whether to reject the null hypothesis. e) Interpret the decision in the context of the original claim. 16) A manufacturer claims that the mean lifetime of its fluorescent bulbs is 1400 hours. A homeowner selects 25 bulbs and finds the mean lifetime to be 1390 hours with a standard deviation of 80 hours. Test the manufacturer's claim. Use = 0.05. a) Identify the claim and state the hypothesis b) Find the critical value and identify the rejection region. c) Find the standardized test statistic t. Sketch a graph. d) Decide whether to reject the null hypothesis. e) Interpret the decision in the context of the original claim.

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