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Alecsey [184]
2 years ago
10

A survey of 85 families showed that 36 owned at least one DVD player. Find the 99% confidence interval estimate of the true prop

ortion of families who own at least one DVD player. Place your limits, rounded to 3 decimal places, in the blanks. Place the lower limit in the first blank
Mathematics
1 answer:
Katyanochek1 [597]2 years ago
3 0

Answer:   (0.367,\ 0.473)

Step-by-step explanation:

The confidence interval for population mean is given by :-

\hat{p}\pm z_{\alpha/2}\sqrt{\dfrac{\hat{p}(1-\hat{p})}{n}}

, where \hat{p} is the sample proportion, n is the sample size , z_{\alpha/2} is the critical z-value.

Given : Significance level : \alpha:1-0.99=0.01

Sample size : n= 85

Critical value : z_{\alpha/2}=2.576

Sample proportion: \hat{p}=\dfrac{36}{85}\approx0.42

Now, the  99% confidence level will be :

\hat{p}\pmz_{\alpha/2}\sqrt{\dfrac{\hat{p}(1-\hat{p})}{n}}\\\\=0.42\pm(2.576)\sqrt{\dfrac{0.42(1-0.42)}{85}}\\\\\approx0.42\pm0.053\\\\=(0.42-0.053,\ 0.42+0.053)=(0.367,\ 0.473)

Hence, the  99% confidence interval estimate of the true proportion of families who own at least one DVD player is  (0.367,\ 0.473)

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