# Relationship among p-value, significance level, and critical

What is the relationship among p-value, significance level, and critical value?

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First a little background on hypothesis tests

When we do a hypothesis test, we first state a null and alternative hypothesis. We then calculate a test statistic that has a known probability distribution if the null hypothesis is true (this is often called the "null distribution". We can think of the test statistic as a randomly selected observation from the null distribution.

If the null hypothesis is true, we therefore expect the value of the test statistic to be a value that is a typical value of the null distribution (not a value very far in one of the tails of the distribution). If the alternative hypothesis is true, we expect to see ...

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This 450 word solution discusses the relationship among p-value, significance level, and critical value.

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%)