Exam 6: Inference for Means and Proportions

Use the following to answer the questions below: An Internet provider contacts a random sample of 300 customers and asks how many hours per week the customers use the Internet. The responses are summarized in the provided dotplot. The average amount of time spent on the Internet per week was 7.2 hours, with a standard deviation of 7.9 hours. ‪ -If we want a margin of error of 0.5 hours, how large of a sample would we need?

Use the following to answer the questions below: Many major television networks air coverage of the incoming election results during primetime hours. The provided boxplot displays the amount of time (in minutes) spent watching election coverage for a random sample of 25 U.S. adults. In this sample, the average time spent watching election coverage was 80.44 minutes with standard deviation of 43.99 minutes. -What sample size would we need to estimate the average amount of time U.S. adults watching election coverage with 99% confidence and a margin of error of ± 5 hours?

Use the following to answer the questions below: Suppose that the makers of M&M's claim that 24% of their Milk Chocolate M&M's are blue. -Assume that bags of Milk Chocolate M&M's labeled as "Medium" size contain 415 candies. Find the standard error of the distribution of sample proportions of blue candies for Medium bags (i.e., samples of size 415). Use four decimal places when reporting the standard error.

Use the following to answer the questions below: In May 2012 President Obama made history by revealing his support of gay marriage. Around that time the Gallup Organization polled 1,024 U.S. adults about their opinions on gay/lesbian relations and gay marriage. They found that 54% of those sampled viewed gay/lesbian relations as "morally acceptable." -Does this sample provide evidence that the majority of U.S. adults (i.e., more than half) believe that gay/lesbian relations are "morally acceptable"? Use a 5% significance level. Verify that the sample size is large enough to use the normal distribution to compute the p-value for this test and include all of the details of the test.

Use the following to answer the questions below: The Math and Verbal SAT scores for a random sample of 10 students from a large introductory statistics course are provided. -Which data analysis method is more appropriate in this situation: paired data difference in means or difference in means with two separate groups?

Use the following to answer the questions below: Consider taking samples of size 100 from a population with proportion 0.33. -Is the sample size large enough for the Central Limit Theorem to apply so that the sample proportions follow a normal distribution?

Use the following to answer the questions below: A small university is trying to monitor its electricity usage. For a random sample of 30 weekend days (Saturdays and Sundays), the student center used an average of 94.26 kilowatt hours (kWh) with standard deviation 43.29. For a random sample of 60 weekdays, (Monday - Friday), the student center used an average of 112.63 kWh with standard deviation 32.07. -Construct a 95% confidence interval for the difference in mean electricity use at the student center between weekdays and weekend days. Use two decimal places in your margin of error.

Use the following to answer the questions below: For each of the following, assume that the sample is a random sample from a distribution that is reasonably normally distributed and that we are doing inference for a population mean. -Find the area in a t-distribution to the left of -2.7 if the sample has size

Use the following to answer the questions below: For each of the following, assume that the sample is a random sample from a distribution that is reasonably normally distributed and that we are doing inference for a population mean. -Find endpoints of a t-distribution with 10% beyond them in each tail if the sample has size

Use the following to answer the questions below: A study published in the American Journal of Health Promotion by researchers at the University of Minnesota (U of M) found that 124 out of 1,923 U of M females had over $6,000 in credit card debt while 61 out of 1,236 males had over $6,000 in credit card debt. -Verify that the sample size is large enough in each group to use the normal distribution to construct a confidence interval for a difference in two proportions.

Use the following to answer the questions below: A sample of 148 college students at a large university reports getting an average of 6.85 hours of sleep last night with a standard deviation of 2.12 hours. -Construct a 98% confidence interval for the average amount of sleep students at this university got last night. Use two decimal places in your margin of error.

Use the following to answer the questions below: The Gallup organization recently conducted a survey of 1,015 randomly selected U.S. adults about "Black Friday" shopping. They asked the following question: "As you know, the Friday after Thanksgiving is one of the biggest shopping days of the year. Looking ahead, do you personally plan on shopping on the Friday after Thanksgiving, or not?" Of the 515 men who responded, 16% said "Yes." Of the 500 women who responded, 20% said "Yes." -Test, at the 5% level, if this sample provides evidence that the proportion of women planning to shop on Black Friday differs significantly from the proportion of men planning to shop. Include all of the details of the test.

Use the following to answer the questions below: An Internet provider contacts a random sample of 300 customers and asks how many hours per week the customers use the Internet. The responses are summarized in the provided dotplot. The average amount of time spent on the Internet per week was 7.2 hours, with a standard deviation of 7.9 hours. ‪ -Construct a 95% confidence interval for the average amount of time customers of this Internet provider spend on the Internet each week. Round the margin of error to one decimal place.

Use the following to answer the questions below: Situations comparing two proportions are described. In each case, determine whether the situation involves comparing proportions for two groups or comparing two proportions from the same group. -Compare the proportion of female students at a university who play a sport to the proportion of male students at a university who play a sport.

Use the following to answer the questions below: A random sample of 48 students at a large university reported getting an average of 7 hours of sleep on weeknights, with standard deviation 1.62 hours. A dotplot of the data is provided. ‪ -Construct a 95% confidence interval for the average amount of weeknight sleep for students at this university. Round the margin of error to two decimal places.

Use the following to answer the questions below: Suppose that the makers of M&M's claim that 24% of their Milk Chocolate M&M's are blue. -Would you expect using bags of Milk Chocolate M&M's labeled as "Large" size, which contain more candies than the "Medium" Size bags, to result in a larger or smaller standard error?

Use the following to answer the questions below: A sample of 148 college students at a large university reports getting an average of 6.85 hours of sleep last night with a standard deviation of 2.12 hours. -Construct a 98% confidence interval for the average amount of sleep students at this university got last night. Provide an interpretation of your interval in the context of this data situation.

Use the following to answer the questions below: Admissions records at a small university indicates that 6.7% of the students enrolled are international students. -Find the mean and standard error of the sample proportion of international students in random samples of size 100. Use four decimal places when reporting the standard error.

Use the following to answer the questions below: Students in a small statistics class were asked to count the number of scars both on their "dominant" hand (the one they use most often) and on their "off" hand. The summary statistics are provided. It is of interest to compare the average number of scars on the dominant and off hands. -Why is it appropriate to use paired data in this analysis? Explain briefly.

Use the following to answer the questions below: In a survey conducted by the Gallup organization, 1,017 adults were asked "In general, how much trust and confidence do you have in the mass media - such as newspapers, TV, and radio - when it comes to reporting the news fully, accurately, and fairly?" Of the 1,017 respondents, 214 said they had "no confidence at all." -Verify that the sample size is large enough to use the normal distribution to construct a confidence interval for the proportion of U.S. adults who have no confidence in the media.