Stat Quiz

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STAT 230 QUIZ 2 Material on Chapters 4, 5 and 6

[1] Mars states that the population proportion of blue M&Ms is .240. When approximating the binomial distribution as NORMAL, what is the probability of calculating a sample proportion of .237 or less blue M&Ms from a sample size of n = 70?

[2] On average, Americans watch 10 complete baseball games per season, with a population standard deviation of 15 games. What is the probability that a sample of 100 Americans watch an average of 12 games or more?

[3] Assume that it is true that people cannot tell the difference between Coke and Pepsi. If a sample of 25 people participated in a blind taste test, can we assume that the sampling distribution of the proportion of people that correctly chose Pepsi is approximately normal? (Why or why not?)

[4] The average length of stay at a local hospital is 4.9 days. Assuming a population standard deviation of 3.5 days, what is the probability a random sample of 50 patients has an average stay of 5.2 days or less?

[5] In an application to estimate the mean number of miles that employees commute to work roundtrip each day, the following information is given: n = 20; sample mean = 4.33; sample standard deviation of s = 3.50 miles. Assuming the parent population is normal, what is the upper limit for a 95 percent confidence interval?

[6] Suppose you want to estimate the population proportion of statistics nerds at UMUC. To do so, you take a sample of 100 students and find that 20 of those students were bona-fide, genuine statistics nerds. What is the lower limit of the 90% confidence interval around your sample proportion?

[7] Assume the GPA of STAT 230 students is distributed normally with a population standard deviation of .10. To test whether the average GPA of Stats II students is GREATER THAN 3.12, a sample of size 49 was drawn and a sample mean of 3.15 was calculated. What is the test statistic?

[8] Using the information from Question [7], what is the p-value?

[9] What is your conclusion to the test in [7] at the 0.05 significance level?

[10] When conducting a hypothesis test, is it possible to keep the probability of a Type I error constant while decreasing the probability of a Type II error?