Exam 10: Estimation and Hypothesis Testing for Two Population Parameters

The Sergio Lumber Company manufactures plywood.One step in the process is the one where the veneer is dried by passing through a huge dryer (similar to an oven)where much of the moisture in the veneer is extracted.At the end of this step,samples of veneer are tested for moisture content.It is believed that pine veneer will be less moist on average than will fir veneer.The following data were reported recently where the values represent the percent moisture in the wood: Based on these data,the critical t value from the t-distribution will be 1.7459 if the significance level is set at 0.05 and variances are presumed equal.

In conducting a hypothesis test for the difference between two population means where the standard deviations are known and the null hypothesis is: H₀ : μ_A - μ_β ≥ 0 What is the p-value assuming that the test statistic has been found to be z = 2.52?

An accounting firm has been hired by a large computer company to determine whether the proportion of accounts receivables with errors in one division (Division 1)exceeds that of the second division (Division 2).The managers believe that such a difference may exist because of the lax standards employed by the first division.The null and alternative hypotheses that will be tested are: H₀ : μ₁ ≥ μ₂ H_a : μ₁ < μ₂

Given the following null and alternative hypotheses H₀ : μ₁ - μ_{2 = 0} H_A : μ₁ - μ_{2 ≠ 0} Together with the following sample information Test the null hypothesis and indicate whether the sample information leads you to reject or fail to reject the null hypothesis,assuming a significance level of 0.05 is to be used.Use the test statistic approach.

In estimating a confidence interval for the difference between two means,when the samples are independent and the standard deviations are unknown,it can be acceptable for there to be small violations of the assumptions of normality and equal variances,especially when the sample sizes are equal.

The t-distribution is still applicable even when there are small violations of the assumptions for the case when the variances for two populations are unknown.This is particularly true when the sample sizes are approximately equal.

When estimating the difference between two population means,when should the normal distribution be used and when should the t-distribution be used?

If we are testing for the difference between the means of two paired populations with samples of n₁ = 20 and n₂ = 20,the number of degrees of freedom is equal to:

A company in Maryland has developed a device that can be attached to car engines,which it believes will increase the miles per gallon that cars will get.The owners are interested in estimating the difference between mean mpg for cars using the device versus those that are not using the device.The following data represent the mpg for random independent samples of cars from each population.The variances are assumed equal and the populations normally distributed. Given this data,what is the upper limit for a 95 percent confidence interval estimate for the difference in mean mpg?

Given the following information,calculate the degrees of freedom that should be used in the pooled-standard deviation t-test.

The National Football League (NFL)is interested in testing to see whether there is a difference in the proportion of male fans that prefer instant replay to review officials' calls and the proportion of female fans that prefer instant replay.It is believed that males tend to favor the practice to a higher degree than do females.To test this,random samples of male fans and female fans were selected and the following results were obtained: Male Fans Female Fans Sample size 300 100 Number Preferring 234 57 Using a significance level equal to 0.05,what conclusion should be reached based on the sample data?

A direct retailer that sells clothing on the Internet has two distribution centers and wants to determine if there is a difference between the proportion of customer order shipments that contain errors (wrong color,wrong size,etc. ).It calculates a 95 percent confidence interval on the difference in the sample proportions to be -0.012 to 0.037.Based on this,it can conclude that the distribution centers differ significantly for the proportion of orders with errors.

If we are testing for the difference between the means of two independent populations with samples of n₁ = 20 and n₂ = 20,the number of degrees of freedom is equal to:

A decision maker wishes to test the following null and alternative hypotheses using an alpha level equal to 0.05: H₀ : μ₁ - μ₂ = 0 H_A : μ₁ - μ₂ ≠ 0 The population standard deviations are assumed to be known.After collecting the sample data,the test statistic is computed to be z = 1.78 Using the test statistic approach,what conclusion should be reached about the null hypothesis?

You are given the following results of a paired-difference test: = -4.6 s_d = 0.25 N = 16 Construct a 99% confidence interval estimate for the paired difference in mean values.

To find the pooled standard deviation involves taking a weighted average of the two sample variances,then finding its square root.

The t-test for the mean difference between 2 related populations assumes that the respective:

A study was recently conducted at a major university to estimate the difference in the proportion of business school graduates who go on to graduate school within five years after graduation and the proportion of non-business school graduates who attend graduate school.A random sample of 400 business school graduates showed that 75 had gone to graduate school while in a random sample of 500 non-business graduates,137 had gone on to graduate school.Based on a 95 percent confidence level,what is the upper limit of the confidence interval estimate?

A paired sample study has been conducted to determine whether two populations have equal means.Twenty paired samples were obtained with the following sample results: Based on these sample data and a significance level of 0.05,what conclusion should be made about the population means?

The Cranston Hardware Company is interested in estimating the difference in the mean purchase for men customers versus women customers.It wishes to estimate this difference using a 95 percent confidence level.Assume that the variances are equal and the populations normally distributed.The following data represent independent samples from each population: Based on these data,the upper limit of the interval estimate is approximately $13.82.