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In: Statistics and Probability

Fear of breast cancer. A recent survey of 1000 American women ages 45-64 asked them what...

Fear of breast cancer. A recent survey of 1000 American women ages 45-64 asked them what medical condition they feared the most. 61% said that they feared breast cancer the most. Construct a 95% confidence interval for the population proportion of women who most feared breast cancer. Then Interpret the confidence interval.

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Expert Solution

Solution :

Given that,

n = 1000

Point estimate = sample proportion = =0.61

1 - = 1-0.61=0.39

At 95% confidence level

= 1 - 95%  

= 1 - 0.95 =0.05

/2 = 0.025

Z/2 = Z0.025 = 1.96 ( Using z table )   

Margin of error = E = Z / 2 * (( * (1 - )) / n)

= 1.96 (((0.61*0.39) / 1000)

E= 0.0302

A 95% confidence interval for population proportion p is ,

- E < p < + E

0.61 -0.0302 < p <0.61+< 0.0302

0.5798< p <0 .6402

The 95% confidence interval for the population proportion p is : 0.5798,0 .6402

orchestra answered 1 year ago
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