A woman and her son are debating about the average length of a preacher's sermons on Sunday

morning. Despite the mother's arguments, the son thinks that the sermons are more than twenty minutes.
For one year, he has randomly selected 12 Sundays and found an average time of 26.42 minutes with a
standard deviation of 6.69 minutes. Assuming that the population is normally distributed and using a 0.05
level of significance, he wishes to determine whether he is correct in thinking that the average length of
sermons is more than 20 minutes. What is the test statistic?
A. –3.32
B. 3.32
C. 0.95
D. 6.69

Z = (score-mean)/SEm

SEm = SD/√n

I'll let you do the calculations.

To determine the test statistic, we need to perform a one-sample t-test.

The test statistic for a one-sample t-test is calculated using the formula:

t = (sample mean - population mean) / (sample standard deviation / sqrt(sample size))

In this case, the sample mean is 26.42 minutes, the population mean we are testing against is 20 minutes, the sample standard deviation is 6.69 minutes, and the sample size is 12 Sundays.

Plugging in these values into the formula:

t = (26.42 - 20) / (6.69 / sqrt(12))

Calculating this expression:

t = 6.42 / (6.69 / 3.464)

t = 6.42 / 1.93

t ≈ 3.32

Therefore, the test statistic is 3.32.

The answer is B. 3.32.

To determine the test statistic, we can perform a one-sample t-test. The test statistic for a one-sample t-test is calculated by dividing the difference between the sample mean and the hypothesized population mean by the standard error of the mean.

In this case, the sample mean is 26.42 minutes, the hypothesized population mean is 20 minutes, and the standard deviation is 6.69 minutes.

The formula for calculating the test statistic is given by:
t = (sample mean - hypothesized population mean) / (standard deviation / sqrt(sample size))

The sample size in this case is 12 Sundays.

Plugging in the values:

t = (26.42 - 20) / (6.69 / sqrt(12))

Calculating this expression gives us:
t = 3.32

Therefore, the test statistic is 3.32.

The answer is B. 3.32.