11.2 Review questions  (Page 2/2)

Explain why we cannot determine the distribution of $X$ .

If you were to create a confidence interval or perform a hypothesis test for the population average checking account balance of 20-year old college students, what distribution would you use?

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

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

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.

REVIEW QUESTION 16 Removed

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 average grade on a math exam in Rachel’s class was 74, with a standard deviation of 5. Rachel earned an 80.
• The average grade on a math exam in Becca’s class was 47, with a standard deviation of 2. Becca earned a 51.
• The average 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, all four quartiles and 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, $P\text{'}$ .

• 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. 10 Californians wear jeans to work and 4 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% level of decision, do you accept or reject the null hypothesis?

• E

  What is the Type I error?

• F

  What is the Type II error?

This is a test of (pick the best answer):

• A

  large samples, independent means

• B

  small samples, independent means

• C

  dependent means

State the distribution to use for the test.