necessaryh
2021-01-05
The sample mean and population standard deviation are provided to you. Use this information to construct the confidence intervals for the population mean. Interpret the results and compare the widths of the confidence intervals.
From a random sample of 66 dates, the mean record high daily temperature in a certain city has a mean of . Assume the population standard deviation is
The confidence interval is
The confidence interval is
Which interval is wider?
Interpret the findings.
Derrick
Skilled2021-01-06Added 94 answers
Step 1
Given:
This mean recorded temperature is:
The population's standard deviation is:
The number of random samples is: dates.
Confidence level :
The confidence level is expressed as,
Step 2
The confidence level can be seen to be symmetric about the P axis in the normal distribution graph. The formula to determine the appropriate value of P is,
From the z-table corresponding to , the value of z is 1.65
The expression to calculate the interval is,
Substitute the values in the above expression.
Therefore, the interval for confidence leven is from 82.928 to 88.452
Step 3
Confidence level
The expression for the confidence level is,
From the graph of the normal distribution, the confidence level is symmetric about the P axis. The expression to calculate the corresponding value of P is,
From the z-table corresponding to , the value of z is 1.96.
The expression to calculate the interval is,
Substitute the values in the above expression.
Hence, the interval for confidence level is from 82.409 to 88.971, and the interval for confidence level is the widest one.
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