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Normal Distribution, Confidence Interval, Test of hypothesis

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1) According to an IRS study, it takes an average of 330 minutes for taxpayers to prepare, copy, and electronically file a 1040 tax form. A consumer watchdog agency selects a random sample of 40 taxpayers and finds the standard deviation of the time to prepare, copy, and electronically file form 1040 is 80 minutes. What assumption or assumptions do you need to make about the shape of the population? What is the standard error of the mean in this example? What is the likelihood the sample mean is greater than 320 minutes? What is the likelihood the sample mean is between 320 and 350 minutes? What is the likelihood the sample mean is greater than 350 minutes?

2) Bob Nale is the owner of Nale's Texaco GasTown. Bob would like to estimate the mean number of gallons of gasoline sold to his customers. From his records, he selects a random sample of 60 sales and finds the mean number of gallons sold is 8.60 and the standard deviation is 2.30 gallons. What is the point estimate of the population mean? Develop a 99 percent confidence interval for the population mean. Interpret the meaning of part b.

3) Dr. Patton is a Professor of English. Recently he counted the number of misspelled words in a group of student essays. For his class of 40 students, the mean number of misspelled words was 6.05 and the standard deviation 2.44 per essay. Construct a 95 percent confidence interval for the mean number of misspelled words in the population of student essays.

4) A sample of 100 observations revealed that p = .75. At the .05 significance level, can the null hypothesis be rejected? State the decision rule. Compute the value of the test statistic. What is your decision regarding the null hypothesis?

5) A sample of 120 observations revealed that p = .30. At the .05 significance level, can the null hypothesis be rejected? State the decision rule. Compute the value of the test statistic. What is your decision regarding the null hypothesis?

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