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# Confidence Intervals an Hypothesis Tests for Mean

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I would like to have the response to the attached problems in excel format so that I can see the formulas used.

Thank you

26. A confidence interval for the price of gasoline from a random sample of 30 gas stations in a region gives the following statistics:
-
y= \$4.49, s=\$0.26

a) Find a 95 % confidence interval for the new price of regular gasoline in that region.
b) Find a 90 % confidence interval for the mean.
c) If we had the same statistics from a sample of 60 stations, what would the 95% confidence interval be now?

28. A company is interested in estimating the costs of lunch in their cafeteria. After surveying employees, the staff calculated that a 95% confidence interval for the mean amount of money spent for lunch over a period of six months is (\$780,\$920). Now the organization is trying to write its repost and considering the following interpretations. Comment on each.

a) 95% of all employees pay between \$780 and \$920 for lunch.
b) 95% of the sampled employees paid between \$780 and \$920 for lunch
c) We're 95% sure that employees in this sample averaged between \$780 and \$920 for lunch.
d) 95% of all samples of employees will have average lunch costs between \$780 and \$920.
e) We're 95% sure that the average amount all employees pay for lunch is \$780 and \$920.

40. A company that produces cell phones claims its standard phone battery lasts longer on average than other batteries in the market. To support this claim, the company publishes an ad reporting the results of a recent experiment showing that under normal usage, their batteries last at least 35 hours. To investigate this claim, a consumer advocacy group asked the company for raw data. The company sends the group the following results:
35, 34, 32, 31, 34, 34, 32, 33, 35, 55, 32, 31
a) Plot the data. Are there any outliners?
b) Find a 95% confidence interval and state your conclusion. Explain how you dealt with the outliner, and why.

https://brainmass.com/statistics/confidence-intervals-hypothesis-tests-mean-561889

#### Solution Preview

Please see the Excel attachment as well.

26. A confidence interval for the price of gasoline from a random sample of 30 gas stations in a region gives the following statistics:Ῡ= \$4.49, s=\$0.26
a) Find a 95 % confidence interval for the new price of regular gasoline in that region."

Step 1: Set the Level of Confidence
Level of confidence =1-a = 0.95

Step 2: Determine the type of distribution to be used
This is a z-Distribution as sample size is 30

Step 3: Calculate the standard error
Observed Mean \$ 4.49
Observed Standard Deviation s \$ 0.26
Number of Observations 30.00
Calculate the Standard Error
0.047

Step 4: Calculate the critical value of test statistics

z -1.960 to 1.960

Step 5: Calculate the confidence interval
Confidence interval from 4.397 to 4.583

b)     Find a 90 % confidence interval for the mean.
Use the same steps to calculate the confidence interval at 90%
Step 1: Set the Level of Confidence
Level of confidence =1-a = 0.90

Step 4: Calculate the critical value of test ...

#### Solution Summary

The confidence intervals for an hypothesis tests for means are provided.

\$2.19