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Education influences attitude and lifestyle. Differences in education are a big factor in the "generation gap." Is the younger generation really better educated? Large surveys of people age 65 and older were taken in *n*_{1} = 30 U.S. cities. The sample mean for these cities showed that *x*_{1} = 15.2% of the older adults had attended college. Large surveys of young adults (age 25–34) were taken in *n*_{2} = 35 U.S. cities. The sample mean for these cities showed that *x*_{2} = 19.7% of the young adults had attended college. From previous studies, it is known that ????_{1} = 7.6% and ????_{2} = 5.8%.

What is the value of the sample test statistic? Compute the corresponding *z* or *t* value as appropriate. (Test the difference ????_{1} − ????_{2}. Round your answer to two decimal places.)

(iii) Find (or estimate) the *P*-value. (Round your answer to four decimal places.)

(b) Find a 90% confidence interval for ????_{1} − ????_{2}. (Round your answers to two decimal places.)

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Here is answer-

To calculate the sample test statistic and the corresponding z-value, we can use the provided information and formulas for testing the difference between two means.

Given:

For the older adults (age 65 and older): Sample size (n1) = 30 Sample mean (x1) = 15.2%

Population standard deviation (????1) = 7.6%

For the young adults (age 25-34):

Sample size (n2) = 35 Sample mean (x2) = 19.7% Population standard deviation (????2) = 5.8%

To test the difference ????1 - ????2, we can calculate the test statistic (t-value) using the formula:

Substituting the given values:

Calculating the value of t will give us the sample test statistic.

Here's a more detailed explanation of the calculations and steps involved:

Sample Test Statistic:

To test the difference ????1 - ????2, we calculate the sample test statistic using the formula:

where x1 and x2 are the sample means, ????1 and ????2 are the population standard deviations, and n1 and n2 are the sample sizes.

Substituting the given values:

Calculate the value of t using this formula. The resulting value will be the sample test statistic.