Question

NCAA rules require the circumference of a softball to be 12 ± 0.125 inches. A softball manufacturer bidding on an NCAA contract is shown to meet the requirements for mean circumference. Suppose that the NCAA also requires that the standard deviation of the softball circumferences not exceed 0.05 inch. A representative from the NCAA believes the manufacturer does not meet this requirement. She collects a random sample of 20 softballs from the production line and finds that s = 0.09 inch. The Anderson-Darling test of normality gives a P-value of 0.729. Is there enough evidence to support the representative’s belief (i.e., that the standard deviation of circumferences exceeds 0.05 inch) at the α = 0.01 level of significance?

Conditions:
a. The χ² ("chi-square") test for standard deviations  (is / is not) appropriate for this data.

Rejection Region:
b. To test the given hypotheses, we will use a _____(left / right / two) -tailed test.  
The appropriate critical value(s) for this test is/are______ .  (Report your answer exactly as it appears in Table VII. For two-tailed tests, report both critical values in the answer blank separated by only a single space.)

c. The test statistic for this test is χ²₀=._______  (Calculate this value in a single step in your calculator, and report your answer rounded to 3 decimal places.)

Label the test statistic in your sketch from Question 3. Use this sketch to conclude the hypothesis test.

d. We_______ (reject / fail to reject) H₀.
e. The given data______ (does / does not) provide significant evidence that the standard deviation of circumferences of softballs from his manufacturer exceeds 0.05 inch.

Answer 1

NULL HYPOTHESIS H0:

ALTERNATIVE HYPOTHESIS Ha:

alpha=0.01

Rejection region: Reject H0 if

test statistic

Degrees of freedom= n-1= 20-1=19

Decision: REJECT H0.

The given data does provide significant evidence that the standard deviation of circumferences of softballs from his manufacturer exceeds 0.05 inch.