Consider the statements of the null and alternative hypotheses below: Ho: HS Ho versus H1: µ > HO On the basis of a random sample, a 95% confidence interval for u is estimated. If the nu hypothesis is not rejected at the 5% significance level, O a. this necessarily implies that Ho is contained in the 95% confidence interval for u O b. All of the suggested answers are correct O c. this necessarily implies that uo is contained in the 95% confidence interval for u provided the observed sample mean is less than O d. this necessarily implies that uo is contained in the 90% confidence interval for u provided the observed sample mean is greater than po e. None of the suggested answers are correct

A corresponding relationship between confidence intervals and two-tailed hypothesis tests also is valid for other parameters, such as p, ?1 − ?2, or p1 − p2, which we will study in later sections.) Whenever the value of k given in the null hypothesis falls outside the c = 1 – α confidence interval for the parameter, we reject H0. For example, consider a two-tailed hypothesis test with ? = 0.01 and H0: ? = 21H1: ? ≠ 21 A random sample of size 30 has a sample mean x = 22 from a population with standard deviation ? = 3. (a) What is the value of c = 1 − ?? Using the methods of Chapter 7, construct a 1 − ? confidence interval for ? from the sample data. (Round your answers to two decimal places.) lower limit       upper limit

2) A 95% confidence interval estimate for a population mean u is (23, 45). Which of the following is a true statement? (A) There is 0.95 probability that µ is between 23 and 45. (B) If 95% confidence intervals are calculated from all possible samples of the given size, µ will be in 95% of these intervals. (C) If 95% confidence intervals are calculated from all possible samples of the given size, 95% of them will be (23, 45). (D) We are 95% confidence that the interval from (23, 45) contains the sample mean i (E) The margin of error of this confidence interval is 22. 3) Last year's AP Statistics class contained 25 students. The class got an average of 71 on the final exam with a sample standard deviation of 4.4. If we assume that this class represents a random sample of all students who have taken AP Statistics and that final exam scores for the population are normally distributed, which of the following is the 96% confidence interval for the true population mean of all AP Statistics…

How does an observed sample mean qualify as a rare outcome?

Suppose that a random sample of 50 bottles of a particular brand of cough syrup is selected and the alcohol content of each bottle is determined. Let u denote the average alcohol content for the population of all bottles of the brand under study. Suppose that the resulting 95% confidence interval is (7.8, 9.4). (a) Consider the following statement: There is a 95% chance that is between 7.8 and 9.4. Is this statement correct? Why or why not? (b) Consider the following statement: We can be highly confident that 95% of all bottles of this type of cough syrup have an alcohol content that is between 7.8 and 9.4. Is this statement correct? Why or why not? (c) Consider the following statement: If the procedure of selecting a sample of size 50 and then computing the corresponding 95% interval is repeated 100 times, approximately 95 of the resulting intervals will include u. Is this statement correct? Why or why not?

Which of the following would be a correct interpretation of a 99% confidence interval such as 4.1 < µ<5.6? Choose the correct answer below. A. We are 99% confident that the interval from 4.1 to 5.6 actually does contain the true value of u. B. It means that 99% of sample means fall between 4.1 and 5.6. C. There is a 99% chance that u will fall between 4.1 and 5.6. D. It means that 99% of all data values are between 4.1 and 5.6.

Based on a random sample of 100 delivery times, the manager of a pizza house obtains the following 99% confidence interval for the average delivery time: (25 minutes, 30 minutes). The manager concludes that at least 99% of the pizzas are delivered in less than 30 minutes and that it will be safe to go ahead with the following special offer:                         "Pizza delivered in 30 minutes or the pizza is free." If the distribution of the population is normal approximately what percentage of the pizzas could be delivered for free in a worse case scenario? This question asks what is the largest possible revenue loss, what is the largest percentage of pizzas that could be delivered for free? Group of answer choices 50% 10% 1% 25%

Sample 1 Assume that both populations are normally distributed. a) Test whether µ, # µ, at the = 0.05 level of significance for the given sample data. b) Construct a 95% confidence interval about u, - H2- Sample 2 17 17 13 14.3 X 3.5 3.1 E Click the icon to view the Student t-distribution table. a) Perform a hypothesis test. Determine the null and alternative hypotheses. CA. Ho: H1 = H2, Hq:Hy # H2 O B. Ho: H1 = H2, H,: H1 Hz Determine the test statistic. t= - 1.15 (Round to two decimal places as needed.) Determine the critical value(s). Select the correct choice below and fill in the answer box(es) within your choice. (Round to three decimal places as needed.) O A. The critical value is O B. The lower critical value is The upper critical value is

Consider a problem of comparing the means of two population means. (If you are using a calculator to obtain answers directly, please write down the steps involved.) For sample 1: ĩi = 10.9, 51 5.4, ni = 15. For sample 2: ã2 = 12.3, 52 = 4.8, n2 = 13. %3D %3D Compute a 95% confidence interval for u1 Mz if both sample 1 and sample 2 are normally distributed; 01 = 02 nevertheless unknown. both sample 1 and sample 2 are normally distributed and we are not sure if ơ1 = 02. both sample 1 and sample 2 are normally distributed and it is given that ơ1 = 02 = 5. both sample 1 and sample 2 are not normally distributed. (Can we actually do it?)

Based on a random sample of size 43, a 93% confidence interval for μ was found to be (24.6, 28.38). This interval will be used to test the following hypotheses: Ho:= 22.3 Ha: 22.3 (a) What is the conclusion? Do not reject the null hypothesis. 22.3 is in the interval, and therefore is one of the plausible values for μ, according to this confidence interval. Reject the null hypothesis. 22.3 is not in the interval, and therefore is not one of the plausible values for μ, according to this confidence interval. Do not reject the null hypothesis. 22.3 is not in the interval, and therefore is not one of the plausible values for μ, according to this confidence interval. O Reject the null hypothesis. 22.3 is in the interval, and therefore is one of the plausible values for μ, according to this confidence interval. (b) What is the significance level of the test? (2 decimal places) (c) How many degrees of freedom are associated with this confidence interval? (whole number)