You are given the sample mean and the population standard deviation. Use this in

Question

You are given the sample mean and the population standard deviation. Use this information to construct the 90% and 95% confidence intervals for the population mean. Which interval is wider? If convenient, use technology to construct the confidence intervals.

A random sample of 44 gas grills has a mean price of $635.70 . Assume the population standard deviation is $56.80 .

The 90% confidence interval is ( ),( )

(Round to one decimal place as needed.)

The 95% confidence interval is ( ).( ).

(Round to one decimal place as needed.)

Which interval is wider? Choose the correct answer below.

The 90% confidence interval

The 95% confidence interval

Explanation / Answer

Here we are given that,

n = sample size = 44

sample mean (Xbar) = $635.70

Population standard deviation (sigma) = $56.80

c = confidence level = 95% and 90% = 0.95 or 0.90

Population standard deviation is known therefore we use Z-Interval.

This we can done by using TI-83 calculator.

steps :

STAT --> TESTS --> 7 : ZInterval --> ENTER --> High light on Stats --> ENTER --> Input sigma, xbar, n and C-level --> Calculate --> ENTER --> ENTER

95% confidence interval for population mean is,

(618.9, 652.5).

length = 652.5 - 618.9 = 33.6

And 90% confidence interval for population mean is,

(621.6, 649.8)

length = 649.8 - 621.6 = 28.1

We can see that as confidence level increases length of confidence interval is also increases.

Large confidence level that is 95% would result in a wider Confidence interval.

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