Question

Question 1.

a) The P-value for a two-sided test of the null hypothesis H0: mu = 30 is 0.08

i.) Does the 95% confidence interval include the value of 30? Explain.

ii.) Does the 90% confidence interval include the value of 30? Explain.

b) A 95% confidence for a population mean is (57,65)

i.) Can you reject the null hypothesis that mu = 68 at the 5% significance level? Explain.

ii.) Can you reject the null hypothesis that mu = 62 at the 5% significance level? Explain.

c) The P-value for a significance test is 0.026

i.) Do you reject the null hypothesis at level alpha = 0.05? Explain.

ii.) Do you reject the null hypothesis at level alpha = 0.01? Explain.

d) What critical value t* should be used to calculate the margin of error for a confidence interval for the mean of the population in each of the following situations? [Hint: To determine the t critical value, we use a t critical value table or calculator. The table/calculator/function uses two values, the significance level and the degree of freedom. The significance level is 100% – 95% = 5% or 0.05. The degree of freedom is n – 1 = 14.]

i.) A 95% confidence interval based on n=15 observations.

ii.) A 95% confidence interval based on n=25 observations.

iii.) A 90% confidence interval based on n=25 observations.

iv.) A 95% confidence interval based on n=101 observations.

e.) The cases in question d) illustrate how the size of the margin of error depends upon the confidence level and sample size. Summarize these relationships.

Answer 1