Question

Please show all work:

Assignment: You will be answering problems #1 - #4. For each problem, you will need to complete parts A through F. Please make sure you answer each part completely and you offer justification where necessary.   Do all work "by hand" (not using StatCrunch) as good practice for your next exam!

A) Write the claim mathematically and state the null and alternative hypotheses.

B) Determine whether the hypothesis test is left-tailed, right-tailed, or two tailed and whether to use a z-test, a t-test, or a chi-square test. Explain your reasoning.

C) Find the critical value(s), draw a sketch identifying the rejection region(s).

D) Find the appropriate standardized test statistic.

E) Decide whether to reject or fail to reject the null hypothesis.

F) Interpret the decision in the context of the original claim.

#3) A restaurant claims that the standard deviation of the lengths of serving times is 3 minutes. A random sample of 27 serving times has a standard deviation of 3.9 minutes. At alpha equal 0.05, is there enough evidence to reject the restaurant's claim?

Answer 1

a)

Below are the null and alternative Hypothesis,
Null Hypothesis, H0: σ = 3
Alternative Hypothesis, Ha: σ ≠ 3

claim is σ = 3

b)

two tailed, chi square test

c)

Rejection Region
This is two tailed test, for α = 0.05 and df = 26
Critical value of Χ^2 are 13.844 and 41.923
Hence reject H0 if Χ^2 < 13.844 or Χ^2 > 41.923

d)

Test statistic,
Χ^2 = (n-1)*s^2/σ^2
Χ^2 = (27 - 1)*3.9^2/3^2
Χ^2 = 43.94

e)

Reject the null hypothesis

f)

There is sufficient evidence to conclude that the standard deviation of the lengths of serving times is 3 minutes