The sample proportion is 0.75 if 98% confidence interval for a proportion is found to be (0.72, 0.78) option (C) is correct.
What is a confidence interval for population standard deviation?
It is defined as the sampling distribution following an approximately normal distribution for known standard deviation.
The formula for finding the confidence interval for population standard deviation as follows:
[tex]\rm s\sqrt{\dfrac{n-1}{\chi^2_{\alpha/2, \ n-1}}} < \sigma < s\sqrt{\dfrac{n-1}{\chi^2_{1-\alpha/2, \ n-1}}}[/tex]
Where s is the standard deviation.
n is the sample size.
[tex]\chi^2_{\alpha/2, \ n-1} and \chi^2_{1-\alpha/2, \ n-1}[/tex] are the constant based on the Chi-Square distribution table:
α is the significance level.
σ is the confidence interval for population standard deviation.
Calculating the confidence interval for population standard deviation:
We know significance level = 1 - confidence level
From the data the margin of error = (0.78 - 0.72)/2
MOE = 0.03
98% Confidence interval for a sample proportion:
n - 0.03 = 0.72
n + 0.03 = 0.78
The interval is (0.72, 0.78)
The sample proportion = 0.75
Thus, the sample proportion is 0.75 if 98% confidence interval for a proportion is found to be (0.72, 0.78) option (C) is correct.
Learn more about the confidence interval here:
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