Question

24

A smart phone manufacturer is interested in constructing a 95% confidence interval for the proportion of smart phones that break before the warranty expires. 85 of the 1622 randomly selected smart phones broke before the warranty expired. Round answers to 4 decimal places where possible.

a. With 95% confidence the proportion of all smart phones that break before the warranty expires is between and .

b. If many groups of 1622 randomly selected smart phones are selected, then a different confidence interval would be produced for each group. About percent of these confidence intervals will contain the true population proportion of all smart phones that break before the warranty expires and about percent will not contain the true population proportion.  

Answer 1

given data are:-

sample size (n) = 1622

sample proportion () = 85/1622 = 0.0524

z critical value for 95% confidence level, both tailed test be:-

a).the 95% confidence interval is:-

With 95% confidence the proportion of all smart phones that break before the warranty expires is between 0.0416 and 0.0632.

b).If many groups of 1622 randomly selected smart phones are selected, then a different confidence interval would be produced for each group. About 95 percent of these confidence intervals will contain the true population proportion of all smart phones that break before the warranty expires and about (100-95) = 5 percent will not contain the true population proportion.  

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