Exam 15: Inference for Counts: Chi-Square

Find expected counts. -Vending machines on a college campus offer a variety of drinks. The purchasing Agent believes that each type of drink is equally preferred by students and consequently Orders equal quantities. The number of drinks sold from vending machines on this Campus for the last six months is shown in the following table. If the purchasing agent is Correct, how many Kiwi Strawberry drinks would we expect to have been sold? Drink Type/Flavor Lemon Lime Sports Drink Kiwi Strawberry Tropical Punch Grape Sports Drink Purchase Frequency 159 198 174 149

Choose the appropriate test. -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? Perfect Parts Co. Made-4-U Co. 25 Hour Parts Co. Rejected 53 48 70 Perfect 93 71 88 Not perfect but acceptable 22 31 22

Find expected counts. -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 Perfect Parts Co. Made-4-U Co. 25 Hour Parts Co. Rejected 53 48 70 Perfect 93 71 88 Not perfect but acceptable 22 31 22

Interpret confidence and prediction intervals. -Determine which type of drink had the most impact on the test results. What are the implications for the purchasing agent?

Create and interpret a confidence interval for the difference of two proportions. -Previous surveys reported that more men than women trade stocks online. A local Brokerage firm randomly selected a sample of investors. They found that 45 out of 234 Men traded online and 42 out of 251 women traded online. The 95% confidence interval For the difference in proportions is

Apply the Chi-Square test of homogeneity. -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 correct value of the test Statistic for determining if the plant manager's belief is supported is Perfect Parts Co. Made-4-U Co. 25 Hour Parts Co. Rejected 53 48 70 Perfect 93 71 88 Not perfect but acceptable 22 31 22 A. $\chi ^ { 2 } = 8.10$ B. $\chi ^ { 2 } = 6.52$ C. $\chi ^ { 2 } = 5.03$ D. $\chi ^ { 2 } = 7.40$ E. $\chi ^ { 2 } = 9.89$

Apply the Chi-Square goodness-of-fit test. -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. With changing demographics, the agency Wondered if the current distribution matches the historical distribution. Recent data Showed the following: Type of Property Condos Townhouses Homes Commercial Land Frequency 89 121 78 25 12 The value of the Chi-square test statistic is A. $\chi ^ { 2 } = 5.993$ B. $\chi ^ { 2 } = 62.538$ C. $\chi ^ { 2 } = 101.482$ D. $\chi ^ { 2 } = 77.431$ E. $\chi ^ { 2 } = 8.101$

Choose the appropriate test. -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. With changing demographics, the agency Wondered if the current distribution matches the historical distribution. Recent data Showed the following: Type of Property Condos Townhouses Homes Commercial Land Frequency 89 121 78 25 12 Which Chi-square test is most appropriate for this situation?

Find expected counts. -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. With changing demographics, the agency Wondered if the current distribution matches the historical distribution. Recent data Showed the following: Type of Property Condos Townhouses Homes Commercial Land Frequency 89 121 78 25 12 Based on the historical distribution, we would expect how many homes to be purchased?

State hypotheses. -Vending machines on a college campus offer a variety of drinks. The purchasing Agent believes that each type of drink is equally preferred by students and consequently Orders equal quantities. The null hypothesis to test his belief can be worded as

Analyze a conclusion using standardized residuals. -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. With changing demographics, the agency Wondered if the current distribution matches the historical distribution. Recent data Showed the following: Type of Property Condos Townhouses Homes Commercial Land Frequency 89 121 78 25 12 What is the standardized residual associated with Townhouses?

Interpret confidence and prediction intervals. -Vending machines on a college campus offer a variety of drinks. The purchasing agent believes that each type of drink is equally preferred by students and consequently orders equal quantities. The number of drinks sold from vending machines on this campus for the last six months is shown in the following table. Drink Type/Flavor Lemon Lime Sports Drink Kiwi Strawberry Tropical Punch Grape Sports Drink 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 = .05.

Create and interpret a confidence interval for the difference of two proportions. -Before being released to market, a drug company tests a new allergy medication for Potential side effects. A random sample of 160 individuals with allergies was selected for The study. The new allergy medication was randomly assigned to 80 of them, and another Popular allergy medication already on the market (Brand C) was assigned to the rest. Out Of the 80 given the new allergy medication, 14 reported drowsiness; 22 of the 80 taking Brand C reported drowsiness. The 95% confidence interval for the difference in Proportions reporting drowsiness is -0.028 to 0.228. Which of the following is correct?

Analyze a conclusion using standardized residuals. -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

Interpret confidence and prediction intervals. -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. With changing demographics, the agency wondered if the current distribution matches the historical distribution. Recent data showed the following: Type of Property Condos Townhouses Homes Commercial Land Frequency 89(48.75) 121(97.5) 78(130) 25(32.5) 12(16.25) 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 = .05.

Interpret confidence and prediction intervals. -An online book store wants to determine if coupon redemption is independent of gender. After a special coupon broadcast to its reward members, the following data on coupon redemption at check out were collected.

Choose the appropriate test. -An online book store wants to determine if there is an association between coupon Redemption and gender. After a special coupon broadcast to its reward members, the Following data on coupon redemption at check out were collected. Which Chi-square test Is most appropriate for this situation? Coupon Redeemed? Yes No Total Sex Male 66 66 132 Female 125 74 199 Total 191 140 331

Find expected counts. -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 perfect Parts from Made-4-U Co. is Perfect Parts Co. Made-4-U Co. 25 Hour Parts Co. Rejected 53 48 70 Perfect 93 71 88 Not perfect but acceptable 22 31 22

Apply the Chi-Square test of independence to test for an association. -An online book store wants to determine if there is an association between coupon Redemption and gender. After a special coupon broadcast to its reward members, the Following data on coupon redemption at check out were collected. The correct value of The test statistic is Coupon Redeemed? Yes No Total Sex Male 66 66 132 Female 125 74 199 Total 191 140 331

Apply the Chi-Square goodness-of-fit test. -Vending machines on a college campus offer a variety of drinks. The purchasing Agent believes that each type of drink is equally preferred by students and consequently Orders equal quantities. The number of drinks sold from vending machines on this Campus for the last six months is shown in the following table. The correct value of the Test statistic for determining if the purchasing agent's belief if supported is Drink Type/Flavor Lemon Lime Sports Drink Kiwi Strawberry Tropical Punch Grape Sports Drink Purchase Frequency 159 198 174 149 A. $\chi ^ { 2 } = 8.012$ B. $\chi ^ { 2 } = 12.019$ C. $\chi ^ { 2 } = 0.984$ D. $\chi ^ { 2 } = 45.014$ E. None of the above.