Question

10. (10 pts) Two brands of refrigerators, Eskimo Choice and Frosty Food, are each guaranteed for 1 year. Each company claims to have the more reliable refrigerator. In a random sample of 50 Eskimo Choice refrigerators, 12 were observed to fail before the guarantee period ended. An independent random sample of 70 Frosty Food refrigerators revealed that 14 refrigerators also failed before the end of the guarantee period. Conduct a hypothesis test to determine if either company can claim to have the more reliable refrigerator at the 0.05 level.

Answer 1

Total number of sample 1 (n1) = 50

Total number of sample 2 (n2) = 70

number of favourable events (X1) = 12

number of favourable events (X2) = 14

We are interested in testing the hypothesis

Decision Rule: Reject the null hypothesis if the test statistic value is greater than the critical value 1.64

The statistic value, 0.5243 is less than the critical values 1.64. Therefore, we fail to reject the null hypothesis.

Frosty Food refrigerators claim to have a more reliable refrigerator at the 0.05 level.