A Fiji Travel Data Center survey reported that Fijians stayed an average of 7.5 nights when they went on vacation around the country. For the purpose of the survey, the sample size was 1500. Assume the population standard deviation was 0.8; find a point estimate of the population mean. In addition, find the 95% confidence interval of the true mean
Answers
Answer:
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Given:
A Fiji Travel Data Center survey reported that Fijians stayed an average of 7.5 nights when they went on vacation around the country.
For the purpose of the survey, the sample size was 1500. Assume the population standard deviation was 0.8;
To find:
Find a point estimate of the population mean.
In addition, find the 95% confidence interval of the true mean
Solution:
From given, we have,
The average mean = x = 7.5
The sample size = n or m = 1500
The standard deviation = σ = 0.8
A point estimate of the population mean.
p = x/m
= 7.5/1500
= 0.005
∴ The point estimate of the population mean is 0.005
The 95% confidence interval of the true mean
The population mean is the true mean.
Calculation
M = 7.5
Z = 1.96
sM = √(0.8²/1500) = 0.02
μ = M ± Z(sM)
μ = 7.5 ± 1.96 × 0.02
μ = 7.5 ± 0.04