Question

The design of an automotive gear requires the diameter to be 4 inches. To evaluate the production quality, you sample 30 gears and find the average to be 4.08 with a standard deviation of 0.71. Construct a hypothesis test at a 0.05 level of significance to determine if the gear diameter is larger than 4 inches.

Select one:

a. The critical value is 1.70, the test statistic is 0.62, conclude the gear diameter is less than or equal to 4 inches

b. The critical value is 1.70, the test statistic is 0.62, conclude the gear diameter is greater than 4 inches

c. The critical value is 2.05, the test statistic is 0.62, conclude the gear diameter is greater than 4 inches

d. The critical value is 2.05, the test statistic is 0.62, conclude the gear diameter is less than or equal to 4 inches

e. The critical value is 2.05, the test statistic is 0.62, conclude the gear diameter is not equal to 4 inches

Answer 1

The correct option is (a)

Given in the question that the average diameter for an automotive gear to be 4 inches. So the sample of 30 gear is collected and their average is and standard deviation as . The significance level for hypothesis test is given as

The null and alternative hypothesis:

; i.e., the average diameter of automotive gear is to be less than or equal to 4 inches.

; i.e., the average diameter of automotive gear is to be greater than 4 inches.

Test-statistic:

Critical value:

Decision:

Since it is a right-tailed hypothesis test, and test statistic is less than the critical value, i.e.,

So, we conclude that at the data does not provide enough evidence to support the alternative hypothesis, i.e., . Hence we FTR(Fail To reject) null hypothesis H₀