Question

Puutage points with 95% contidence. 6. A random sample of 37 suspension-type football helmets were subjected to an impact test. Twenty-four helmets showed damage after the test. Construct a 94% confidence interval for the true proportion of all helmets of this type that would show damage after being in the impact test.

Answer 1

It seems you did correct work .

n = 37

x =24

$\hat{p}=\frac{x}{n}= \frac{24}{37}=0.6486$

c- level = 0.94

Critical value for 94% confidence

             (rounded to 2 decimal )

Confidence interval formula:

$\hat{p}\pm Z_{0.03} \sqrt{\frac{\hat{p}*(1-\hat{p})}{n}}$

$0.6486\pm 1.88 \sqrt{\frac{0.6486*(1-0.6486)}{37}}$

$0.6486\pm 1.88 \sqrt{\frac{0.22791804 }{37}}$

$0.6486\pm 1.88 \sqrt{0.006159947}$

0.6486 +1.88 +0.07848533

$0.6486\pm 0.14755242$

Answer :

We are 94% Confidence interval that the true proportion of all helmates of this type that would show damge after being in the inpact test between