Exam 10: Hypothesis Testing: Additional Topics

A production manager is interested in comparing the precision of two brands of stamping machines.From a random sample of 12 units of output from the Brand A machine,a standard deviation of 15.2 is reported for a quality characteristic.For the Brand B machine,in a sample of 20 units of output,there is a standard deviation of 10.1.Is there sufficient evidence at the 5% significance level to conclude that Brand B machines have a lower variance in quality? Assume that the quality characteristic of both machines follows a normal distribution.

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION: As part of its quality control program,the Scullia Auto Company (SAC)began inspecting all supplier shipments of steel bars and recording the defect rate according to quality criteria such as strength,dimensional characteristics,etc.When SAC began this program,the defect rate in 100 shipments averaged 9%.A recent report indicated an average defect rate of 2.2% in 136 shipments.The quality control department wants to determine,at the 0.05 level of significance,if this represents a significant improvement in the quality of the steel. -At the 0.05 level of significance,what conclusion can be drawn,from the hypothesis test,about the quality improvement in the Scullia Auto Company?

Consider independent random samples from two normally distributed populations.The first population has a mean of μ_x and a variance of and we obtain a random sample of size n_x.The second population has a mean of μ_y and a variance of And we obtain a random sample of size n_y.The sample means are denoted by And )Which of the following formulae calculates the random variable,Z?

State the null and alternative hypotheses to determine if the mean score of medical students differs from the mean score of law students.

In testing H₀ : P_x - P_y = 0,an estimate of the common population proportion is a weighted average of the two sample proportions,the weights being equal to the sample sizes.

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION: The sociological department of Kent College conducted an investigation to determine how long it takes for a woman or man to get married after their graduation in Kent Town.Two independent random samples were selected and the following summary information concerning times to completion of medical school were computed: -State the appropriate null and alternative hypotheses to determine whether there is a significant difference in time to completion of medical school between women and men.

If two population variances are known,the test for differences in the two population means does not require the populations to be normally distributed if the sample sizes are large.

The F distribution is constructed as the ratio of two random variables following a ________ distribution.

Given the following information, = 4, = 6,n₁ = 15,n₂ = 20,calculate the degrees of freedom that should be used in the pooled-variance t test.

Consider a standard model with a random sample of n_x observations from a population with a proportion P_x of successes and a second independent random sample of n_y observations from a population with a proportion P_y of successes.Which of the following formulas illustrates normally distributed random variables when testing the difference between two population proportions?

The sample size in each independent sample must be the same if we are to test for differences between the means of two independent populations.

The test for the equality of two population variances assumes that each of the two populations is normally distributed.

The ________ is constructed as the ratio of two chi-square random variables,each divided by its degrees of freedom.

National Park rangers were surveyed as to whether they endorsed the idea of carrying firearms.Of the 260 rangers polled west of the Tanahousie,78% endorsed the idea.Of the 184 rangers polled east of the Tanahousie,64% endorsed the idea.Is there evidence that the level of support for carrying firearms is different in the west than it is in the east of Tanahousie? (Assume 10% significance level)

When testing for the differences between the means of two independent populations,only a two-tailed test can be used.

What is the value of α,if the cutoff point for an F distribution F_9,23 = 2.32?

If the null hypothesis H₀ : μ_x - μ_y ≥ 0 is rejected against the alternative H₁ : μ_x - μ_y < 0 at the 2% level of significance,then using the same data,it must be rejected against that alternative at the 3% level.

What is the cutoff point for an F distribution with 20 numerator degrees of freedom and 30 denominator degrees of freedom at α = 0.05? (Hint: Round your answer to 2 decimal places. )

The t test for the difference between the means of two independent populations assumes that the respective:

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION: The following data were generated from a matched pairs experiment. -State the appropriate null and alternative hypotheses to determine whether the two population means differ at 10% significance level.