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b. Now suppose the sample consists of 35 girls instead of 15. Repeat the test Determine the null and altenative hypotheses. Choose the correct choice below. C. Hạ 542 OA. Ho: 54.2 Hyi 54.2 Hi u> 54.2 Hi 54.2 OE HS42 H54.2 OF HoieS42 OD. H >42 H54.2 Hi54.2 Find the test statistic - -0.68 (Round to two decimal places as needed.) Find the p-value. p- (Round to three decimal places as needed.)

b. Now suppose the sample consists of 35 girls instead of 15. Repeat the test Determine the null and altenative hypotheses. Choose the correct choice below. C. Hạ 542 OA. Ho: 54.2 Hyi 54.2 Hi u> 54.2 Hi 54.2 OE HS42 H54.2 OF HoieS42 OD. H >42 H54.2 Hi54.2 Find the test statistic - -0.68 (Round to two decimal places as needed.) Find the p-value. p- (Round to three decimal places as needed.)

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN:9780079039897
Author:Carter
Publisher:Carter
Chapter10: Statistics
Section10.5: Comparing Sets Of Data
Problem 14PPS
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In County A, the population mean height for 10-year-old girls is 54.2 inches with a standard deviation of 2.1 inches. Suppose a random sample of 15 10-year-old girls from Country B is taken, and these girls had a sample mean height of 53.9 inches with a standard deviation of 2.6 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: - A. \( H_0: \mu = 54.2 \) \( H_a: \mu \neq 54.2 \) - B. \( H_0: \mu \neq 54.2 \) \( H_a: \mu = 54.2 \) - C. \( H_0: \mu = 54.2 \) \( H_a: \mu > 54.2 \) - D. \( H_0: \mu \neq 54.2 \) \( H_a: \mu < 54.2 \) - E. \( H_0: \mu = 54.2 \) \( H_a: \mu < 54.2 \) - F. \( H_0: \mu > 54.2 \) \( H_a: \mu = 54.2 \) - *(The correct choice is A: \( H_0: \mu = 54.2 \), \( H_a: \mu \neq 54.2 \))* - Check the conditions to see whether the test statistic will follow a t-distribution: The sample is ___ random and the observations ___ are ___ independent. The distribution of the heights is ___ **Normally distributed**. - Find the test statistic: \( t = -0.45 \) **(Round to two decimal places as needed.)** - Find the p-value: \( p = 0.662 \) **(Round to three decimal places as needed.)** - Interpret the results of the test: Since the p-value is ___ greater than ___ the
Transcribed Image Text:In County A, the population mean height for 10-year-old girls is 54.2 inches with a standard deviation of 2.1 inches. Suppose a random sample of 15 10-year-old girls from Country B is taken, and these girls had a sample mean height of 53.9 inches with a standard deviation of 2.6 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: - A. \( H_0: \mu = 54.2 \) \( H_a: \mu \neq 54.2 \) - B. \( H_0: \mu \neq 54.2 \) \( H_a: \mu = 54.2 \) - C. \( H_0: \mu = 54.2 \) \( H_a: \mu > 54.2 \) - D. \( H_0: \mu \neq 54.2 \) \( H_a: \mu < 54.2 \) - E. \( H_0: \mu = 54.2 \) \( H_a: \mu < 54.2 \) - F. \( H_0: \mu > 54.2 \) \( H_a: \mu = 54.2 \) - *(The correct choice is A: \( H_0: \mu = 54.2 \), \( H_a: \mu \neq 54.2 \))* - Check the conditions to see whether the test statistic will follow a t-distribution: The sample is ___ random and the observations ___ are ___ independent. The distribution of the heights is ___ **Normally distributed**. - Find the test statistic: \( t = -0.45 \) **(Round to two decimal places as needed.)** - Find the p-value: \( p = 0.662 \) **(Round to three decimal places as needed.)** - Interpret the results of the test: Since the p-value is ___ greater than ___ the
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