Question

1.) A sample of 125 campus students who responded to a questionnaire had a mean age of 22.0 and a standard deviation of 5.0. The mean hypothesized population age for all campus students is 25.0.

a)  Set up the hypothesis (one sample t test) for these data at the 95% confidence level. Be sure to include the null hypothesis and alternative hypothesis in your response.

b) Compute the t test statistic for these data.

c) Are you able to reject the null hypothesis, or are you unable to reject it?

d) Calculate the confidence interval for the true population mean at the 95% confidence level.

2.)

For the identical scenario, now set your confidence level at 99%.

a) Are you able to reject the null hypothesis, or are you unable to reject it?

b) Calculate the confidence interval for the true population mean at the 99% confidence level.

Answer 1

Answer:

1.

Given,

Ho : u = 25

Ha : u != 25

test statistic = (x - u)/(s/sqrt(n))

substitute values

= (22 - 25)/(5/sqrt(125))

t = - 6.71

degree of freedom = n - 1

= 125 - 1

= 124

P value <= 0.00001

Here p value < alpha, so we reject Ho. There is not sufficient evidence.

t(alpha/2,df) = t(0.025 , 124) = 1.98

CI = xbar +/- t*s/sqrt(n)

substitute values

= 22 +/- 1.98*5/sqrt(125)

= 22 +/- 0.8855

= (21.1145 , 22.8855)

Please post the remaining question as separate post. Thank you.