In Country A, the population mean height for 10-year-old girls is 54.8 inches with a standard deviation of 2.2 inches. Suppose a random sample of 15 10-year-old girls from Country B is taken and that these girls had a sample mean height of53.3 inches with a standard deviation of 2.8 inches. Assume that heights are Normally distributed. Complete parts (a) through (c) below.b. Now suppose the sample consists of 50 girls instead of 15. Repeat the test.Determine the null and alternative hypotheses. Choose the correct choice below.O A. Ho: µ = 54.8Ha: µ> 54.8О В. Но: и> 54.8Hai µ= 54.8Ос. Но: и 54.8Ha: u#54.8ОЕ. Но: и#54.8Ha: µ= 54.8O D. Ho: u = 54.8O F. Ho: u< 54.8Ha:H< 54.8Ha: µ= 54.8Find the test statistic.t= (Round to two decimal places as needed.)Find the p-value.p= (Round to three decimal places as needed.)Interpret the results of the test.Sinahe valuV ianificance leveeviaeneto conclude that the neight or 1 vear-old airlsrom untay Pi sightficantly differenromCo A popultion me atSignificance level of 005.c. Explain why the t-values and p-values for parts a and b are different. Choose the correct answer below.O A. Alarger n causes a smaller standard error (narrower sampling distribution) with less area in the tails, as shown by the larger p-value.O B. A larger n causes a smaller standard error (narrower sampling distribution) with less area in the tails, as shown by the smaller p-value.OC. A larger n causes a larger standard error (wider sampling distribution) with more area in the tails, as shown by the larger p-value.O D. Alarger n causes a larger standard error (wider sampling distribution) with less area in the tails, as shown by the smaller p-value.

Given: Population Mean μ=54.8 Sample Size n=15 Sample Standard Deviation s=2.8 Sample Mean X¯=53.3

In Country A, the population mean height for 10-year-old girls is 54.8 inches with a standard deviation of 2.2 inches. Suppose a random sample of 15 10-year-old girls from Country B is taken and that these girls had a sample mean height of 53.3 inches with a standard deviation of 2.8 inches. Assume that heights are Normally distributed. Complete parts (a) through (c) below. b. Now suppose the sample consists of 50 girls instead of 15. Repeat the test. Determine the null and alternative hypotheses. Choose the correct choice below. O B. Ho: >54.8 OC. Ho: = 54.8 O A. Ho: u= 54.8 Hiu> 54.8 O D. Ho: u= 54.8 H:u<54.8 H:u= 54.8 H: u#54.8 O E. Ho: µ#54.8 Hip= 54.8 OF. Ho: <54.8 HiH =54.8 Find the test statistic. t= (Round to two decimal places as needed.) Find the p-value. p= O(Round to three decimal places as needed.) Interpret the results of the test. Con conclude that the ta gnicantly nificance level of 5. c. Explain why the t-values and p-values for parts a and b are different. Choose the correct answer below. O A. Alarger n causes a smaller standard error (narrower sampling distribution) with less area in the tails, as shown by the larger p-value. O B. Alarger n causes a smaller standard error (narrower sampling distribution) with less area in the tails, as shown by the smaller p-value. OC. Alargern causes a larger standard error (wider sampling distribution) with more area in the tails, as shown by the larger p-value. O D. Alarger n causes a larger standard error (wider sampling distribution) with less area in the tails, as shown by the smaller p-value.

18th Edition

ISBN:9780079039897

Author:Carter

Publisher:Carter

Chapter10: Statistics

Section10.4: Distributions Of Data

Problem 19PFA