0.1 Review exercises (ch 3-13)  (Page 9/12)

108. Find the 95% confidence interval for the true mean checking account balance of a twenty-year-old college student.

109. What type of data is the balance of the checking account considered to be?

110. What type of data is the number of twenty-year-olds considered to be?

111. On average, a busy emergency room gets a patient with a shotgun wound about once per week. We are interested in the number of patients with a shotgun wound the emergency room gets per 28 days.

1. Define the random variable X .
2. State the distribution for X .
3. Find the probability that the emergency room gets no patients with shotgun wounds in the next 28 days.

Use the following information to answer the next two exercises: The probability that a certain slot machine will pay back money when a quarter is inserted is 0.30. Assume that each play of the slot machine is independent from each other. A person puts in 15 quarters for 15 plays.

112. Is the expected number of plays of the slot machine that will pay back money greater than, less than or the same as the median? Explain your answer.

113. Is it likely that exactly eight of the 15 plays would pay back money? Justify your answer numerically.

114. A game is played with the following rules:

• it costs $10 to enter.
• a fair coin is tossed four times.
• if you do not get four heads or four tails, you lose your $10.
• if you get four heads or four tails, you get back your $10, plus $30 more.

115.

• The mean grade on a math exam in Rachel’s class was 74, with a standard deviation of five. Rachel earned an 80.
• The mean grade on a math exam in Becca’s class was 47, with a standard deviation of two. Becca earned a 51.
• The mean grade on a math exam in Matt’s class was 70, with a standard deviation of eight. Matt earned an 83.

Use the following information to answer the next two exercises: A random sample of 70 compulsive gamblers were asked the number of days they go to casinos per week. The results are given in the following graph:

116. Find the number of responses that were five.

117. Find the mean, standard deviation, the median, the first quartile, the third quartile and the IQR .

118. Based upon research at De Anza College, it is believed that about 19% of the student population speaks a language other than English at home. Suppose that a study was done this year to see if that percent has decreased. Ninety-eight students were randomly surveyed with the following results. Fourteen said that they speak a language other than English at home.

1. State an appropriate null hypothesis.
2. State an appropriate alternative hypothesis.
3. Define the random variable, P ′.
4. Calculate the test statistic.
5. Calculate the p -value.
6. At the 5% level of decision, what is your decision about the null hypothesis?
7. What is the Type I error?
8. What is the Type II error?

119. Assume that you are an emergency paramedic called in to rescue victims of an accident. You need to help a patient who is bleeding profusely. The patient is also considered to be a high risk for contracting AIDS. Assume that the null hypothesis is that the patient does not have the HIV virus. What is a Type I error?