Determine the null and alternative hypotheses. Choose the correct answer below. O A. Ho: u= 54.8 Hgiµ#54.8 О в. Но: и 54.8 H: µ> 54.8 O. Họ: u= 54.8 Hg:µ<54.8 O E. Ho: u> 54.8 Ha: = 54.8 OF. Ho: u<54.8 H μ 54.8 O D. Ho: u#54.8 Hạ: u= 54.8 Check the conditions to see whether the test statistic will follow a t-distribution. The sample V random and the observations independent. The distribution of the heights is Find 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. Since the p-value is V the significance level, V Ho. There is V evidence to conclude that the height for 10-year-old girls from Country B is significantly different from the Country A population mean at significance level of 0.05.

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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.
О В. Но: и> 54.8
Ha: u= 54.8
Ос. Но: и 54.8
Ha: u#54.8
О А. Но: и 54.8
Hai u> 54.8
O D. Ho: u= 54.8
Ha: H< 54.8
O E. Ho: u#54.8
Ha: µ = 54.8
O F. Hoμ< 54.8
Ha: u= 54.8
Find 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.
Since the p-value is
V the significance level,
V Ho. There is
V evidence to conclude that the height for 10-year-old girls from Country B is significantly different from the Country A population mean a
significance level of 0.05.
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. 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. Alargern causes a larger standard error (wider sampling distribution) with less area in the tails, as shown by the smaller p-value.
Transcribed Image Text: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. О В. Но: и> 54.8 Ha: u= 54.8 Ос. Но: и 54.8 Ha: u#54.8 О А. Но: и 54.8 Hai u> 54.8 O D. Ho: u= 54.8 Ha: H< 54.8 O E. Ho: u#54.8 Ha: µ = 54.8 O F. Hoμ< 54.8 Ha: u= 54.8 Find 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. Since the p-value is V the significance level, V Ho. There is V evidence to conclude that the height for 10-year-old girls from Country B is significantly different from the Country A population mean a significance level of 0.05. 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. 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. Alargern causes a larger standard error (wider sampling distribution) with less area in the tails, as shown by the smaller p-value.
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.
a. Determine whether the population mean for height for 10-year-old girls from Country B is significantly different from the Country A population mean. Use a significance level of 0.05.
Determine the null and alternative hypotheses. Choose the correct answer below.
O A. Ho: µ= 54.8
Ос. Но: р354.8
О В. Но: и 54.8
Hai u> 54.8
Ha: u#54.8
Hạ: H< 54.8
O D. Ho: µ#54.8
Ha: H = 54.8
O E. Ho: µ> 54.8
Ha: µ = 54.8
OF. Ho: H< 54.8
Hạ: µ = 54.8
Check the conditions to see whether the test statistic will follow a t-distribution.
The sample
V random and the observations
V independent. The distribution of the heights is
Find 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.
Since the p-value is
V the significance level,
Ho. There is
V evidence to conclude that the height for 10-year-old girls from Country B is significantly different from the Country A population mean at
significance level of 0.05.
Transcribed Image Text: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. a. Determine whether the population mean for height for 10-year-old girls from Country B is significantly different from the Country A population mean. Use a significance level of 0.05. Determine the null and alternative hypotheses. Choose the correct answer below. O A. Ho: µ= 54.8 Ос. Но: р354.8 О В. Но: и 54.8 Hai u> 54.8 Ha: u#54.8 Hạ: H< 54.8 O D. Ho: µ#54.8 Ha: H = 54.8 O E. Ho: µ> 54.8 Ha: µ = 54.8 OF. Ho: H< 54.8 Hạ: µ = 54.8 Check the conditions to see whether the test statistic will follow a t-distribution. The sample V random and the observations V independent. The distribution of the heights is Find 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. Since the p-value is V the significance level, Ho. There is V evidence to conclude that the height for 10-year-old girls from Country B is significantly different from the Country A population mean at significance level of 0.05.
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