FORESTRY
AGRICULTURAL STATISTICS AND ECONOMICS
Question
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A study found that in a sample of 44 subjects, 9 of them agree that children under 6 shouldn’t be taken to nice restaurants.The 95% confidence interval for p is (0.082, 0.318). Interpret this interval.

95% of the time the proportion of people who believe children under 6 shouldn’t be taken to nice restaurants will be between 8.2% and 31.8%.


The population proportion of people who believe children under 6 shouldn’t be taken to nice restaurants is between 8.2% and 31.8%.


The probability that the proportion of people who believe children under 6 shouldn’t be taken to nice restaurants will be between 8.2% and 31.8% is 95%.


Based on this sample, I am 95% confident that the proportion of people who believe children under 6 shouldn’t be taken to nice restaurants is between 8.2% and 31.8%.

Explanation:
Detailed explanation1: The value of z* for a confidence level of 95% is 1.96.
Detailed explanation2: The critical zscore values when using a 95 percent confidence level are1.96 and +1.96 standard deviations. The uncorrected pvalue associated with a 95 percent confidence level is 0.05.
Detailed explanation3: To calculate the confidence interval, we must find p′, q′. p′ = 0.842 is the sample proportion; this is the point estimate of the population proportion. Since the requested confidence level is CL = 0.95, then = 1 – CL = 1 – 0.95 = 0.05 ( 2 ) ( 2 ) = 0.025.
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