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Based on the sample data...

Based on the sample data, a confidence interval has been constructed such that we have 95% confidence that the population mean is between 83 and 103. What conclusion would be reached at the α = .05 level in testing H0: μ = 95 versus H1: μ; ≠ 95?

_________________

Use the information given to find the lower and upper critical values for the sample mean:n = 1077

σ = 64.87

μ = 458.52

α = 0.10 (Round your answer(s) to 3 decimal places.) Lower value = _________

Upper value = _________

Find the critical value of the sample mean for the given situation: H0: μ; ≥ 500

H1: μ 836; α = 0.05

Compute the test statistic. (Round your answer(s) to 3 decimal places.) Appropriate test: _________________

Test statistic = _________

A soft drink dispenser is set to automatically dispense drinks and ice in 8 oz. cups. The machine is set to fill the cups with 7 1/4 oz. so that the liquid will not run over the top of the cup. The company is getting complaints that the machine is filling the cups too full and spilling over. When the machine is operating properly, only 1% of the cups will not be filled properly. The production manager conducted a one-tail hypothesis test at the 0.01 level to check the machine. A sample of 45 fills was measured. For the critical z, identify the sample proportion that this z-value represents. (Round your answer(s) to 4 decimal places.)

p = _________

A large bank in a metropolitan area has a large number of secured loans on apartment facilities throughout the area. Local economic indicators suggest the percentage of vacant apartments ranges from 7% to 12%. Concerned about the borrowers’ ability to meet loan obligations on time the bank decides to sample from the apartments used to secure loans. The officer responsible for the sample decides to allow a maximum error of the estimate of 0.01 with 99 percent confidence. The officer wishes to take a sample large enough to cover all proportions within the estimated vacancy range. Compute the sample size needed for this study. (Round your answer(s) to 3 decimal places.)

_________

During the last energy crisis, a government official claimed that the average car owner refilled the tank when there was more than 3 gallons left. To check the claim, 10 cars were surveyed as they entered a gas station. The amount of gas was measured and recorded as follows:

3, 2, 6, 4, 2, 5, 3, 1, 3, 3

If we assume that the amount of gas remaining in tanks is normally distributed with a

standard deviation of one gallon, can we conclude at the 10% significance level that the official was correct? (Round your answer(s) to 2 decimal places.)

Appropriate test: _________________

Test statistic = _________

Conclusion: _________________ Interpretation: _________________

For a sample of 37 items from a population for which the standard deviation σ = 13, the sample mean is 340. Construct a 95% confidence interval for the population mean. (Round your answer(s) to 2 decimal places.)

95% CI = _________ to _________

_________________

Use the information given to find the lower and upper critical values for the sample mean:n = 1077

σ = 64.87

μ = 458.52

α = 0.10 (Round your answer(s) to 3 decimal places.) Lower value = _________

Upper value = _________

Find the critical value of the sample mean for the given situation: H0: μ; ≥ 500

H1: μ 836; α = 0.05

Compute the test statistic. (Round your answer(s) to 3 decimal places.) Appropriate test: _________________

Test statistic = _________

A soft drink dispenser is set to automatically dispense drinks and ice in 8 oz. cups. The machine is set to fill the cups with 7 1/4 oz. so that the liquid will not run over the top of the cup. The company is getting complaints that the machine is filling the cups too full and spilling over. When the machine is operating properly, only 1% of the cups will not be filled properly. The production manager conducted a one-tail hypothesis test at the 0.01 level to check the machine. A sample of 45 fills was measured. For the critical z, identify the sample proportion that this z-value represents. (Round your answer(s) to 4 decimal places.)

p = _________

A large bank in a metropolitan area has a large number of secured loans on apartment facilities throughout the area. Local economic indicators suggest the percentage of vacant apartments ranges from 7% to 12%. Concerned about the borrowers’ ability to meet loan obligations on time the bank decides to sample from the apartments used to secure loans. The officer responsible for the sample decides to allow a maximum error of the estimate of 0.01 with 99 percent confidence. The officer wishes to take a sample large enough to cover all proportions within the estimated vacancy range. Compute the sample size needed for this study. (Round your answer(s) to 3 decimal places.)

_________

During the last energy crisis, a government official claimed that the average car owner refilled the tank when there was more than 3 gallons left. To check the claim, 10 cars were surveyed as they entered a gas station. The amount of gas was measured and recorded as follows:

3, 2, 6, 4, 2, 5, 3, 1, 3, 3

If we assume that the amount of gas remaining in tanks is normally distributed with a

standard deviation of one gallon, can we conclude at the 10% significance level that the official was correct? (Round your answer(s) to 2 decimal places.)

Appropriate test: _________________

Test statistic = _________

Conclusion: _________________ Interpretation: _________________

For a sample of 37 items from a population for which the standard deviation σ = 13, the sample mean is 340. Construct a 95% confidence interval for the population mean. (Round your answer(s) to 2 decimal places.)

95% CI = _________ to _________

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