Question

#9 and #10 in detail please!

7. For females, what is the proportion that exercise regularly? Chart of exercise 20 15 Cound 9. Define the parameter being estimated. 10. State and check the assumptions for the 95% confidence interval for the population proportion. Make sure to explain why the assumptions are met or not. A check mark is not sufficient. If an assumption is not met explain what this means for the validity of the confidence interval. (2 points) (I want you to compute the interval and interpret even if the assumption is not met, to show that you know how to do it if the assumptions had been met.)

Answer 1

9

No. of females that exercise = 21

No. of females that do not exercise = 9

Probability of females that exercise = 21/30 = 0.7

10.

CI for proportion using t-test as sample size is small = 30.

$\hat p \pm \sqrt{\frac{p*q}{n}}*t_{\alpha/2}$

Now, p = 0.7, q = 0.3, n = 30 and at n = 30 and df = 29 and alpha = 0.05, t = Critical value (2-tailed) = CI

Assumptions:

• independent observations
• random observations
• population normally distributed
• variances are equal

Sample size is small nd hence we use t-test and assume other conditions.

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