Question:
Problem 9.17: The average age of first-time brides reportedly has increased during the past two decades. By 1993, the average age of a first-time bride was about 24.5 years. Suppose you want to test this figure, because you believe the average age is younger than that now. You take a random sample of 19 first-time brides this year and obtain the following data (in years).

Given:
22 17 24 26 25 28 21 19 35 32 28 22 21 19 20 18 19 22 24

According to these data, is there enough evidence to reject the claim for 1993 as too high for this year? Assume ages of first-time brides are normally distributed and use alpha of 0.10.

Given: = 24.5 years = average age of a first-time brides.

Step 1:
Hypothesis is that the average age of a first-time bride is less than 24.5 years, but since this is an unproven theory, it is the alternate hypothesis. The null hypothesis is that the mean is still 24.5 years

Ho : =24.5
Ha : <24.5

Step 2: The statistical test to be used is

Step 3: The value of alpha is 0.10

Step 4: With 19 data points, df = (n-1) = 19 - 1 = 18. The test is one-tailed, and the critical table t-value is:
t0.10,18 =- 1.33

Step 5: Consider sample data above

Step 6:
23.26316 = sample mean
4.817123 = sample standard deviation





t = -1.12

Answer:

Step 7: Computed t value of -1.12 is greater than table t value of -1.33, therefore we fail to reject null hypothesis. Value is within non rejection area. Average age of first time brides is indeed 24.5.

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