Let’s say you wish to construct a sampling distribution of sample size 100 for the proportion of people that voted for AAP. Suppose the population standard deviation is known to be 0.7, what is the interval in which the mean of the sampling distribution will belong at a 90% confidence level?(0.485, 0.675) (0.572, 0.588)(0.465, 0.695)(0.503, 0.657)
Question
Let’s say you wish to construct a sampling distribution of sample size 100 for the proportion of people that voted for AAP. Suppose the population standard deviation is known to be 0.7, what is the interval in which the mean of the sampling distribution will belong at a 90% confidence level?(0.485, 0.675) (0.572, 0.588)(0.465, 0.695)(0.503, 0.657)
Solution
To construct a sampling distribution of sample size 100 for the proportion of people that voted for AAP, we need to determine the interval in which the mean of the sampling distribution will belong at a 90% confidence level.
Given that the population standard deviation is known to be 0.7, we can use the formula for the margin of error to calculate the interval. The margin of error is given by:
Margin of Error = Z * (Standard Deviation / √Sample Size)
For a 90% confidence level, the Z-value is 1.645 (obtained from the standard normal distribution table). Plugging in the values, we have:
Margin of Error = 1.645 * (0.7 / √100) = 1.645 * (0.7 / 10) = 0.11415
To find the interval, we subtract and add the margin of error to the sample proportion. Let's denote the sample proportion as p̂.
Interval = (p̂ - Margin of Error, p̂ + Margin of Error)
Since we don't have the sample proportion, we cannot calculate the exact interval. However, we can determine which of the given options contains the interval by comparing the calculated margin of error with the range of each option.
Looking at the options provided: (0.485, 0.675) (0.572, 0.588) (0.465, 0.695) (0.503, 0.657)
We can see that the interval (0.503, 0.657) contains the calculated margin of error of 0.11415. Therefore, the correct interval at a 90% confidence level is (0.503, 0.657).
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