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 4.11 with a standard deviation of 0.67. 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 2.05, the test statistic is 0.90, conclude the gear diameter is not equal to 4 inches

b. The critical value is 2.05, the test statistic is 0.90, conclude the gear diameter is greater than 4 inches

c. The critical value is 2.05, the test statistic is 0.90, conclude the gear diameter is less than or equal to 4 inches

d. The critical value is 1.70, the test statistic is 0.90, conclude the gear diameter is less than or equal to 4 inches

e. The critical value is 1.70, the test statistic is 0.90, conclude the gear diameter is greater than 4 inches

Answer 1

Null hypothesis

vs

Alternative hypothesis

T test for single mean

=0.90

Sample size =30

Degree of freedom =n-1 = 30-1 =29

t critical value is 1.70 ......................by using t table.

t calculated value =0.90 < t critical value =1.70

Therefore, we fail to reject H0 at

Option d) is correct.

d. The critical value is 1.70, the test statistic is 0.90, conclude the gear diameter is less than or equal to 4 inches