11.7 The chi-square distribution: review  (Page 2/2)

What type of data is the number of 20 year olds considered to be?

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.

• a Define the random variable $X$ .
• b State the distribution for $X$ .
• c Find the probability that the emergency room gets no patients with shotgun wounds in the next 28 days.

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.

Is it likely that exactly 8 of the 15 plays would pay back money? Justify your answer numerically.

A game is played with the following rules:

• it costs $10 to enter
• a fair coin is tossed 4 times
• if you do not get 4 heads or 4 tails, you lose your $10
• if you get 4 heads or 4 tails, you get back your $10, plus $30 more

Over the long run of playing this game, what are your expected earnings?

• The mean grade on a math exam in Rachel’s class was 74, with a standard deviation of 5. Rachel earned an 80.
• The mean grade on a math exam in Becca’s class was 47, with a standard deviation of 2. Becca earned a 51.
• The mean grade on a math exam in Matt’s class was 70, with a standard deviation of 8. Matt earned an 83.

Find whose score was the best, compared to his or her own class. Justify your answer numerically.

Find the number of responses that were “5".

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

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.

• a State an appropriate null hypothesis.
• b State an appropriate alternate hypothesis.
• c Define the Random Variable, $\hat{p}$ .
• d Calculate the test statistic.
• e Calculate the p-value.
• f At the 5% level of decision, what is your decision about the null hypothesis?
• g What is the Type I error?
• h What is the Type II error?

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?

It is often said that Californians are more casual than the rest of Americans. Suppose that a survey was done to see if the proportion of Californian professionals that wear jeans to work is greater than the proportion of non-Californian professionals. Fifty of each was surveyed with the following results. 15 Californians wear jeans to work and 6 non-Californians wear jeans to work.

• $C$ = Californian professional
• $\text{NC}$ = non-Californian professional

• a State appropriate null and alternate hypotheses.
• b Define the Random Variable.
• c Calculate the test statistic and p-value.
• d At the 5% significance level, what is your decision?
• e What is the Type I error?
• f What is the Type II error?