Stats Study Sheet

1. Assume 20% of all email is spam. A large Internet provider plans on conducting a survey of 900 emails to see what percentage are spam. a. What is the probability they will get a proportion greater than 0. 1836? b. If they get a sample proportion over 24% they are going to shut down their email server. What is the probability this will happen? 2. A survey is done to estimate the proportion of U. S. adults who think that cell phone use while driving should be illegal. In the survey, 54% of a randomly selected sample of 1025 individuals said that cell phone use while driving should be illegal. a.

What is the 90% confidence interval for the proportion of adults who think cell phone use should be illegal? 1. A sample of college students was asked whether they would return the money if they found a wallet on the street. Of the 93 women, 84 said “yes,” and of the 75 men, 53 said “yes. ” Assume that these students represent all college students (Data source is from UC Davis and can be found in the textbook). a. Is there enough data to calculate a confidence interval for the women? 2. A sample of college students was asked whether they would return the money if they found a wallet on the street.

Of the 93 women, 84 said “yes,” and of the 75 men, 53 said “yes. ” Assume that these students represent all college students (Data source is from UC Davis and can be found in the textbook). b. Is there enough data to calculate a confidence interval for the women? 3. A CNN/Time poll conducted in the United States October 23-24, 2002, (http://www. pollingreport. com) asked, “Do you favor or oppose the legalization of marijuana? ” In the nationwide poll of n = 1007 adults, 34% said that they favored legalization. a.

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A sample of 500 women using oral contraceptives showed 15% had high blood pressure A sample of 400 women not using oral contraceptives showed 10% had high blood pressure. b. What is the 92% confidence interval for the difference in the two proportions? (using – not using) b. If the magazine had wanted to get a margin of error of only 1%, at least how many adults should they have interviewed? 1. University of Wyoming policy states that you should spend 6 hours a week on homework. To find out how close our class is we randomly sample 100 students from class and ask, “How many hours do you spend on homework each week? The mean for the 100 responses is 3. 6 hours with a standard deviation of 0. 7 hours (sample statistic). Find a 95% confidence interval for the true average. * We use 80 degrees of freedom, because (1) t-table does not have t-values for 99 degrees of freedom and also because using 100 degrees of freedom is too liberal. The reason is that we can never say we have more data than you really do; OK to say you have less. * We use t-table and not z-table because our standard deviation has been computed from sample values. 7.

The center for disease control wants to know the average life span of an ebola virus. Studies of similar types of viruses suggest the standard deviation will be 2. 55 days (population parameter: use z-table), but they want a 99% confidence interval for the true average lifespan, and they want that confidence interval to have a width of 0. 5 days. How many ebola viruses do they need to sample? •We can use z-table instead of t-table because the standard deviation comes from the population. ¬ •We can use z-table instead of t-table because the standard deviation comes from the population. 7.

The center for disease control wants to know the average life span of an ebola virus. Studies of similar types of viruses suggest the standard deviation will be 2. 55 days (population parameter: use z-table), but they want a 99% confidence interval for the true average lifespan, and they want that confidence interval to have a width of 0. 5 days. How many ebola viruses do they need to sample? •We can use z-table instead of t-table because the standard deviation comes from the population. ¬ •We can use z-table instead of t-table because the standard deviation comes from the population. 9.

Example 11. 12 (p. 428) studies hangover symptoms in college students (Slutske et al. , 2003). The students answered questions about alcohol use and hangovers, including a count of how many out of a list of 13 possible hangover symptoms that they had experienced in the past year. For the 470 men, the mean number of symptoms was 5. 3; for the 755 women, it was 5. 1. The standard deviation was 3. 4 for each of the two samples. a. Find a 95% confidence interval for the difference in population means. 9. Example 11. 12 (p. 428) studies hangover symptoms in college students (Slutske et al. 2003). The students answered questions about alcohol use and hangovers, including a count of how many out of a list of 13 possible hangover symptoms that they had experienced in the past year. For the 470 men, the mean number of symptoms was 5. 3; for the 755 women, it was 5. 1. The standard deviation was 3. 4 for each of the two samples. a. Find a 95% confidence interval for the difference in population means. 3. In each part, use the information given to calculate the margin of error. a. A sample of n = 81 women has standard deviation 2. 7 inches. Confidence90%

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