Q.3 (Show your computations) The U.S. Energy Administration reported that the mean price for a gallon of regular gasoline in the United States was 236.7 cents (U.S. Energy Administration, January 30, 2018). Population Data for regular gasoline prices (cents per gallon) of all 60 service stations in the Lower Atlantic states are contained in the Minitab data file into variable-named Gasoline price. a.) Using Minitab to select a random sample of 32 observations from this population, indicate the random sample of 32 observations, sample mean and sample standard deviation. b.) (1) Formulate the hypotheses that can be used to determine whether the mean price for a gallon of gasoline in the Lower Atlantic states is different from the national mean. (ii) Assume o = 5.4. Indicate an appropriate test statistic and compute its value based on the obtained sample mean in question a.). What are the p-value and your conclusion at a=7%? (iii) Assume o = 5.4. Compute a (100-7) % confidence interval for the population mean gasoline price for your sample of 32 observations. Q.4 (9 marks) (Show your computations) Refer to the obtained data in Q.3., let be the sample proportion of 32 gasoline prices that greater than 236.7 cents per gallon. a.) (2.5 marks) Indicate the random sample proportion of 32 observations and compute the sample proportion. (b.) (4.5 marks) It has been found that 30% of all service stations in the Lower Atlantic state will have the gasoline prices are greater than 236.7 cents per gallon. At a=7%, is there sufficient evidence to conclude that the sample proportion differs from the national percentage? Use the p-value method. (c.)(2 marks) Find a (100-7) % confidence interval of the true proportion. Q.5 Using Minitab in data analysis and answer the questions The dean of students wants to see whether there is a significant difference in ages of resident students and commuting students. She selects a sample of 14 students from each population. Two population data are contained in the Minitab data file into variable-named Resident and Commuter. a.) Using Minitab to select a random sample of 14 observations from each population, indicate the random sample of 14 observations, sample mean and sample standard deviation for each population. b.) Refer to the obtained data in a.), conduct a hypothesis to test the difference between the population variance of ages between the two groups. Given a=9%. c.) Refer to the results from b.), conduct a hypothesis to test the difference between the population mean of ages between resident students and commuting students. Given a=9%. d.) What is the (100-9% confidence interval for the difference between two populations mean ages of resident students and commuting students. Q.6 Using Minitab in data analysis and answer the questions The amount of income spent on housing is an important component of the cost of living. The total costs of housing for homeowners might include mortgage payments, property taxes, and utility costs (water, heat, electricity). Suppose that an economist collected all of 30 homeowners in a district and then calculated these total housing costs as a percent of monthly income, five years ago and now. The population information is reported and contained in the Minitab data file into variable-named Five years ago and Now. a.) Using Minitab to select a random sample of 13 observations from the population, indicate the random sample of 13 observations b.) Is it reasonable to conclude the percent is less now than five years ago? Given a= = 7% (i) State the null and alternative hypotheses. (ii) What is the test statistic? (iii) What is the p-value? (iv) What are the sample mean differences and the sample standard deviation of the differences? (v) What is the conclusion? c.) (2marks) Provide a (100-7) % confidence interval for the mean increase in listening score due to the intensive training. Q.3 (Show your computations) The U.S. Energy Administration reported that the mean price for a gallon of regular gasoline in the United States was 236.7 cents (U.S. Energy Administration, January 30, 2018). Population Data for regular gasoline prices (cents per gallon) of all 60 service stations in the Lower Atlantic states are contained in the Minitab data file into variable-named Gasoline price. a.) Using Minitab to select a random sample of 32 observations from this population, indicate the random sample of 32 observations, sample mean and sample standard deviation. b.) (1) Formulate the hypotheses that can be used to determine whether the mean price for a gallon of gasoline in the Lower Atlantic states is different from the national mean. (ii) Assume o = 5.4. Indicate an appropriate test statistic and compute its value based on the obtained sample mean in question a.). What are the p-value and your conclusion at a=7%? (iii) Assume o = 5.4. Compute a (100-7) % confidence interval for the population mean gasoline price for your sample of 32 observations. Q.4 (9 marks) (Show your computations) Refer to the obtained data in Q.3., let be the sample proportion of 32 gasoline prices that greater than 236.7 cents per gallon. a.) (2.5 marks) Indicate the random sample proportion of 32 observations and compute the sample proportion. (b.) (4.5 marks) It has been found that 30% of all service stations in the Lower Atlantic state will have the gasoline prices are greater than 236.7 cents per gallon. At a=7%, is there sufficient evidence to conclude that the sample proportion differs from the national percentage? Use the p-value method. (c.)(2 marks) Find a (100-7) % confidence interval of the true proportion. Q.5 Using Minitab in data analysis and answer the questions The dean of students wants to see whether there is a significant difference in ages of resident students and commuting students. She selects a sample of 14 students from each population. Two population data are contained in the Minitab data file into variable-named Resident and Commuter. a.) Using Minitab to select a random sample of 14 observations from each population, indicate the random sample of 14 observations, sample mean and sample standard deviation for each population. b.) Refer to the obtained data in a.), conduct a hypothesis to test the difference between the population variance of ages between the two groups. Given a=9%. c.) Refer to the results from b.), conduct a hypothesis to test the difference between the population mean of ages between resident students and commuting students. Given a=9%. d.) What is the (100-9% confidence interval for the difference between two populations mean ages of resident students and commuting students. Q.6 Using Minitab in data analysis and answer the questions The amount of income spent on housing is an important component of the cost of living. The total costs of housing for homeowners might include mortgage payments, property taxes, and utility costs (water, heat, electricity). Suppose that an economist collected all of 30 homeowners in a district and then calculated these total housing costs as a percent of monthly income, five years ago and now. The population information is reported and contained in the Minitab data file into variable-named Five years ago and Now. a.) Using Minitab to select a random sample of 13 observations from the population, indicate the random sample of 13 observations b.) Is it reasonable to conclude the percent is less now than five years ago? Given a= = 7% (i) State the null and alternative hypotheses. (ii) What is the test statistic? (iii) What is the p-value? (iv) What are the sample mean differences and the sample standard deviation of the differences? (v) What is the conclusion? c.) (2marks) Provide a (100-7) % confidence interval for the mean increase in listening score due to the intensive training
Answer & Explanation
Solved by verified expert
Get Answers to Unlimited Questions
Join us to gain access to millions of questions and expert answers. Enjoy exclusive benefits tailored just for you!
Membership Benefits:
Unlimited Question Access with detailed Answers
Zin AI - 3 Million Words
10 Dall-E 3 Images
20 Plot Generations
Conversation with Dialogue Memory
No Ads, Ever!
Access to Our Best AI Platform: Flex AI - Your personal assistant for all your inquiries!
