Question

11-26: a computer manufacturer offers technical support that is available 24 hours a day, 7 days a week. timely resolution of these calls is important to the company's image. for 35 calls that were related to software, technicians resolved the issues in a mean time of 18 minutes with a standard deviation of 4.2 minutes. for 45 calls related to hardware, technicians resolved the problems in a mean time of 15.5 minutes with a standard deviation of 3.9 minutes. at the .05 significance level, does it take longer to resolve software issues? a. what are the null and alternate hypotheses? b. compute the test statistic. c. compute the p-value. d. what is your decision regarding the null hypothesis? e. interpret the result.

Answer 1

The question is asking to determine if it takes longer to resolve software issues compared to hardware issues. The null and alternative hypotheses are stated, and steps are provided to compute the test statistic and p-value. The decision regarding the null hypothesis is made based on the p-value, and the result is interpreted.

Step-by-step explanation:

a. Null hypothesis: The mean time to resolve software issues is equal to or less than the mean time to resolve hardware issues.
Alternate hypothesis: The mean time to resolve software issues is greater than the mean time to resolve hardware issues.

b. To compute the test statistic, we will use the formula:
Test statistic = (sample mean 1 - sample mean 2) / sqrt((standard deviation 1^2 / sample size 1) + (standard deviation 2^2 / sample size 2))
Test statistic = (18 - 15.5) / sqrt((4.2^2 / 35) + (3.9^2 / 45))

c. To compute the p-value, we will use the test statistic and the degrees of freedom to look up the p-value in a t-distribution table or use a t-distribution calculator.

d. Based on the p-value obtained in step c, we will compare it to the significance level (0.05) to make a decision regarding the null hypothesis. If the p-value is less than 0.05, we reject the null hypothesis. If the p-value is greater than or equal to 0.05, we fail to reject the null hypothesis.

e. If we reject the null hypothesis, it means that there is enough evidence to suggest that it takes longer to resolve software issues compared to hardware issues. If we fail to reject the null hypothesis, it means that there is not enough evidence to conclude that it takes longer to resolve software issues.