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(Solved): Education influences attitude and lifestyle. Differences in education are a big factor in the "gener ...


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 n1 = 30 U.S. cities. The sample mean for these cities showed that x1 = 15.2% of the older adults had attended college. Large surveys of young adults (age 25–34) were taken in n2 = 35 U.S. cities. The sample mean for these cities showed that x2 = 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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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.


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