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# The Significance Level and Estimate P-Value

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"A recent article in The Wall Street Journal reported that the 30-year mortgage rate is now less than 6 percent. A sample of eight small banks in the Midwest revealed the following 30-year rates (in percent):
"
4.8 5.3 6.5 4.8 6.1 5.8 6.2 5.6
At the .01 significance level, can we conclude that the 30-year mortgage rate for small banks is less than 6 percent?
The significance level is 0.01.
estimate the p-value.

Exercise 27 - A recent study focused on the number of times men and women who live alone buy take-out dinner in a month. The information is summarized below.

Statistic Men Women
Sample mean 24.51 22.69
Population standard deviation 4.48 3.86
Sample size 35.00 40.00

At the .01 significance level, is there a difference in the mean number of times men and women order take-out dinners in a month?

Exercise 46 - Grand Strand Family Medical Center is specifically set up to treat minor medical emergencies for visitors to the Myrtle Beach area. There are two facilities, one in the Little River Area and the other in Murrells Inlet. The Quality Assurance Department wishes to compare the mean waiting time for patients at the two locations. Samples of the waiting times, reported in minutes, follow:

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#### Solution Summary

The significance level and estimates p-value are examined.

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## Formulate an 84% interval estimate for a true proportion

1) The Target Corporation personnel director wants to estimate the number of employees within one year of retirement. A random sample of 120 employee records is selected, and 36 people are found to be within one year of retirement. Formulate an 84% interval estimate for the true proportion of employees within one year of retirement in the entire corporation.

2) As a quality control expert, you want to estimate the mean thickness of optical lenses produced by your firm. A sample of 144 lenses reveals a mean of 0.52 millimeters (mm). The population standard deviation is known to be 0.17 mm. Construct a 95% confidence interval.

3) As the new manager for a CPA firm, you want to establish the confidence interval for the time to complete a medium sized organization's tax return. A sample of 25 medium corporate accounts is selected at random. The sample mean and standard deviation are 20 days and 4 days, respectively. Using a confidence interval of 90%, construct the interval.

4) A manufacturer of detergent claims that the mean weight of a particular box of detergent is at least 3.25 pounds. A random sample of 81 boxes reveals a sample average of 3.18 pounds and a sample standard deviation of 0.15 pounds. Using a 0.10 level of significance, is there evidence that the average weight of the boxes is different from at least 3.25 pounds as stated above?

5) A package-filling device is set to fill cereal boxes with a mean weight of 20 ounces of cereal per box. The population standard deviation for the filling machine is 0.5 ounces. A random sample of 25 filled boxes is weighed, yielding a mean weight of 20.27 ounces. Test at the 0.05 significance level to determine whether the device is working properly.

6) The manager of the credit department for an oil company would like to determine whether the average monthly balance of credit card holders is greater than \$75. An auditor selects a random sample of 100 accounts and finds that the average owed is \$83.40 with a population standard deviation of \$23.65. Using the 0.05 level of significance, should the auditor conclude that there is evidence that the average balance is greater than \$75?

7) Linear Regression

Below is the printout for a regression of crop yield on rainfall, fertilizer, and soil acidity.

Predictor B Coef Stdev Beta

Constant 3.3
Rain 0.23 0.1588 0.2508
Fertilizer 1.15 0.2772 0.7714
Acid -0.113 0.1093 -0.0935

S= 6.4987 r-sq = 0.9283 r-sq (adj) = 0.9087

Using the computer results for the regression analysis answer the following:

a. Write the equation to describe the model. (5%)
b. Explain the relationships between fertilizer and crop yield. (6%)
c. Is the relationship between soil acidity a direct or inverse relationship? (5%)
d. Is this a model a good fit and justify your response? (6%)
e. What is the adjusted coefficient of determination and explain what it means .(6%)

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