8. A random sample of 28 independent female college-aged dancers showed a sample

Question

8. A random sample of 28 independent female college-aged dancers showed a sample mean height of 62.9 inches and a sample standard deviation of 1.8 inches. Assume that this distribution of heights is Normal Complete parts a through c below. a. Use technology to find a 95% confidence interval for the population mean height of dancers and interpret the interval Choose the correct answer below and if necessary fill in the answer boxes to complete your choice A. We are 95% confident that the population mean height of all dancers is between and B. We are 95% confident that the population mean height of female college-aged dancers is between ° C. We are 95% confident that the sample mean height of female college-aged dancers is between O D. The requirements for constructing a confidence interval are not satisfied and and Type integers or decimals rounded to the nearest tenth as needed. Use ascending order.) b Use technology to find a 99% confidence interval or the population mean height and interpret the interval Choose the correct answer below and if necessary fill in the answer boxes to complete your choice O A. We are 99% confident that the population mean height of female college-aged dancers is between O B. We are 99% confident that the population mean height of all dancers is between and and C. We are 99% confident that the sample mean height of female college-aged dancers is between and O D. The requirements for constructing a confidence interval are not satisfied Type integers or decimals rounded to the nearest tenth as needed. Use ascending order.) c. Which interval is wider and why? O A. The 95% interval is wider because it has a lower confidence level, and therefore we use a bigger value oft, which creates a wider interval value of t, which creates a wider interval of t. which creates a wider interval of t, which creates a wider interval. O B. The 99% interval is wider because it has a greater confidence level, and therefore we use a smaller C. The 99% interval is wider because it has a greater confidence level, and therefore we use a bigger value O D. The 95% interval is wider because it has a lower confidence level, and therefore we use a smaller value

Explanation / Answer

Ans:

a)critical t value for 95% CI and df=28-1=27 is 2.052

95% CI for mean

=62.9+/-2.052*1.8/sqrt(28)

=62.9+/-0.698

=(62.2, 63.6)

Option B is correct.

b)critical t value for 99% CI and df=28-1=27 is 2.771

95% CI for mean

=62.9+/-2.771*1.8/sqrt(28)

=62.9+/-0.943

=(62.0, 63.8)

Option A is correct.

c)As,the confidence level increases,t* value increases and CI becomes wider.

so,99% CI is wider than 95% CI.

Option C is correct.

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