Exam 13: Inference for Counts: Chi-Square Tests

A manufacturer of cordless electric shavers sampled 13 from a day's production and found the mean time of continuous usage without recharging to be 410 minutes with a Sample standard deviation of 30 minutes. We can assume that times are normally Distributed. We wish to test if the true mean operating time without recharging is more Than 400 minutes. The correct null and alternative hypotheses are

A manufacturing plant for recreational vehicles receives shipments from three different parts vendors. There has been a defect issue with some of the electrical wiring in the Recreational vehicles manufactured at the plant. The plant manager believes that the Defect issue is dependent on the parts vendor. The plant manager reviews a sample of Quality assurance inspections from the last six months. Which Chi-square test is most Appropriate for this situation?

A sample of 30 year fixed mortgage rates at 12 randomly chosen credit unions yields a mean rate of 6.65 % and a sample standard deviation of 0.38%. A sample of 30 year Fixed mortgage rates at 16 randomly selected banks yields a mean rate of 7.05% and a Sample standard deviation of 0.22%. Are the mean rates different between credit unions And banks? Relevant output is shown below. At the 0.05 level of significance, the Correct conclusion is Two-Sample T-Test and $\mathbf { C l }$ Sample Mean StDev SE Mean 1 12 6.650 0.390 0.11 2 16 7.050 0.220 0.055 Difference $= m u$ (1) $- \mathrm { mu }$ (2) Bstimate for difference: $- 0.400$ $95 \%$ CI for difference: $( - 0.666 , - 0.134 )$ $T$ -Test of difference $= 0$ (vs not $= ) : T$ -Value $= - 3.19$ p-Value $= 0.006 \quad \mathrm { DF } = 16$

A local politician was interested in determining whether income level affects opinion regarding the government's bailout bill for easing the 2008 financial crisis on Wall Street. He surveyed a sample of his constituents and got the following results. The calculated Value of the Chi Square statistic is

A sample of 30 year fixed mortgage rates at 12 randomly chosen credit unions yields a mean rate of 6.65 % and a sample standard deviation of 0.38%. A sample of 30 year Fixed mortgage rates at 16 randomly selected banks yields a mean rate of 7.05% and a Sample standard deviation of 0.22%. Are the mean rates different between credit unions And banks? Relevant output is shown below. Which of the following is true? Sample Mean StDev SE Mean 1 12 6.650 0.390 0.11 2 16 7.050 0.220 0.055 Difference $= m u ( 1 ) = m u$ (2) Bstimate for difference: $\quad - 0.400$ 95 옿 CI for difference: $( - 0.666 , - 0.134 )$ T-Test of difference $= 0$ (vs not $= ) :$ T-Value $= - 3.19$ P-Value $= 0.006 \quad$ DF $= 16$

The weights of soy patties sold by Veggie Burgers Delight are normally distributed. A random sample of 15 patties yields a mean weight of 3.8 ounces with a sample Standard deviation of 0.5 ounces. At the 0.05 level of significance, perform a hypothesis Test to see if the true mean weight is less than 4 ounces. The correct conclusion at the 0.05 level of significance is

Chris Columbus is responsible for controlling inventory levels for four types of sailboats sold by his company. Chris takes a sample of 48 boats sold over the past Several months to determine if demand is the same for each type. His results are as Follows: Type of Boat Sales Pirate's Revenge 15 Jolly Roger 11 Sails Delight 10 Cruiser Cove 12 The correct null hypothesis to be tested is

Which of the following is not an assumption or condition that needs to be checked for a two-sample t-test for the difference between two means?

Shape-Up-By-Susie claims that participating in her exercise program will result in guaranteed weight loss in just 6 weeks. Five clients weighed themselves before and then Again after participating in her program and the differences "weight after - weight Before" were analyzed. Based on the relevant computer output shown below, we can say Paired T for After - Before Mean StDev SE Mean After 5 144.6 31.7 14.2 Before 5 148.0 28.9 12.9 Difference 5 -3.40 3.51 1.57 $95 \%$ upper bound for mean difference: $- 0.06$ $\mathrm { T }$ -Test of mean difference $= 0 ( \mathrm { vs } < 0 ) : \mathrm { T }$ -Value $= - 2.17 \mathrm { P }$ -Value $= 0.048$

A contact lens wearer read that the producer of a new contact lens boasts that their hypothesis $H _ { 0 } : \mu _ { \text {old } } - \mu _ { \text {new } } = 0$ is tested against the alternative $H _ { A } : \mu _ { \text {old } } - \mu _ { \text {new } } > 0$ . Which of the following would be a Type II error?

Vending machines on a college campus offer a variety of snacks. The purchasing agent believes that each type of snack is equally preferred by students and consequently orders equal quantities. The number of snacks sold from vending machines on this campus for the last six months is shown in the following table. Snack Type Chips Candy Bars Crackers Nuts Purchase Frequency 159 198 174 149 A. State appropriate hypotheses to test whether the purchasing agent is correct. b. What is the value of the test statistic and its associated P-value? c. State the conclusion at α = .05.

An army depot that overhauls ground mobile radar systems is interested in improving its processes. One problem involves troubleshooting a particular component that has a High failure rate after it has been repaired and reinstalled in the system. The shop floor Supervisor believes that having standard work procedures in place will reduce the time Required for troubleshooting this component. Time (in minutes) required troubleshooting This component without and with the standard work procedure is recorded for a sample of 19 employees. Assuming that we define our differences as Time without standard work Procedure - Time with standard work procedure, the correct alternative hypothesis is

By examining residuals, determine which type of snack had the most impact on the test results? What are the implications for the purchasing agent?

Vending machines on a college campus offer a variety of drinks. The purchasing agent believes that each type of snack is equally preferred by students and consequently orders Equal quantities. The number of snacks sold from vending machines on this campus for The last six months is shown in the following table. The P-value of the calculated Chi- Square statistic is 0.0458. At α = 0.05, we should Snack Type Chips Candy Bars Crackers Nuts Purchase Frequency 159 198 174 149

Which factor listed below does not affect the power of a test?

A professor was interested in determining whether the prices of new textbooks in the bookstore were higher than if purchased online. She selected 6 textbooks and priced each At the bookstore and online. Paired T for Bookstore - Online Mean StDev SE Mean Bookstore 6 115.00 22.36 9.13 Online 6 105.83 13.20 5.39 Difference 6 9.17 13.20 5.39 $95 \div$ lower bound for mean difference: $- 1.69$ T-Test of mean difference $= 0 ( \mathrm { vs } > 0 ) : \mathrm { T }$ -Value $= 1.70 \mathrm { P }$ -Value $= 0.075$ Based on her analysis, we can conclude at the 0.05 level of significance that

A real estate agency, located in a metropolitan area in the northeastern U.S., kept data on the various types of properties purchased in the area. Historically, 15% of purchases Were for condominiums, 30% were for townhouses, 40% for single family homes, 10% For commercial properties and 5% for land. Based on the data shown below, the null Hypothesis was rejected and the agency concluded that the current distribution of property Sales differs from the historical distribution. Based on an examination of the standardized Residuals, which type of property had the most impact on the test results? Type of Property Condos Townhouses Homes Commercial Land Frequency 89 121 78 25 12

Vending machines on a college campus offer a variety of snacks. The purchasing agent believes that each type of snack is equally preferred by students and consequently Orders equal quantities. The number of snacks sold from vending machines on this Campus for the last six months is shown in the following table. The appropriate test to See if the purchasing agent is correct is the Snack Type Chips Candy Bars Crackers Nuts Purchase Frequency 159 198 174 149

A manufacturing plant for recreational vehicles receives shipments from three different parts vendors. There has been a defect issue with some of the electrical wiring in the Recreational vehicles manufactured at the plant. The plant manager believes that the Defect issue is dependent on the parts vendor. The plant manager reviews a sample of Quality assurance inspections from the last six months. The expected number of rejected Parts from Perfect Parts Co. is

Chris Columbus is responsible for controlling inventory levels for four types of sailboats sold by his company. Chris takes a sample of 48 boats sold over the past Several months to determine if demand is the same for each type. His results are as Follows: Type of Boat Sales Pirate's Revenge 15 Jolly Roger 11 Sails Delight 10 Cruiser Cove 12 The calculated value of the Chi Square statistic is