Question

Refer to the following scenario to answer questions #3 through #5.

According to the most recent 2018 estimates from the U.S. Census Bureau, the average age of first marriage for women is approximately 28 years old. You think that this number is much too low. You randomly sample 12 women and conduct a single sample t test to determine whether the known value of 28 for the population is significantly different from the mean score for the sample.

Ages of women for a random sample: 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 38, 40

Question 3

What is the mean for the sample?

Question 4

What is the value of t? (round to the thousandths)

Question 5

The difference between the population mean of 28 and the mean of the sample is statistically significant at the .05 level.

Group of answer choices

True

False

Answer 1

From the given sample data ; n=12 , ,

The sample mean is ,

The sample standard deviation is ,

Hypothesis: VS  

The test is two-tailed test.

Since , the population standard deviation is not known.

Therefore , use t-distribution.

Now , df=degrees of freedom=n-1=12-1=11

The critical value is ,

; From t-table

The value of t is ,

Decision : Here , the vaue of test statistic t=4.088 lies in the rejection region.

Therefore , reject Ho.

Conclusion : Hence , the difference between the population mean of 28 and the mean of the sample is statistically significant