# homework part 2

10. At a factory that produces pistons for cars, Machine 1 produced satisfactory pistons and unsatisfactory pistons today. Machine 2 produced satisfactory pistons and unsatisfactory pistons today. Suppose that one piston from Machine 1 and one piston from Machine 2 are chosen at random from today’s batch. What is the probability that the piston chosen from Machine 1 is satisfactory and the piston chosen from Machine 2 is unsatisfactory ?

11. A survey showed that 23% of college students read newspapers on a regular basis and that 81% of college students regularly watch the news on TV. The survey also showed that 21% of college students both follow TV news regularly and read newspapers regularly.

(a) What is the probability that a randomly selected college student reads newspapers regularly, given that he or she watches TV news regularly? Round your answer to 2 decimal places.

(b) What is the probability that a student watches TV news regularly, given that he or she regularly reads newspapers? Round your answer to decimal places.

A=

B=

13. Let be a random variable with the following probability distribution:

Value x of X P(X=x)

10 .10

20 .65

30 .10

40 .05

50 .10

E(x)=

Var(X)=

14. Suppose that the New England Colonials baseball team is equally likely to win any particular game as not to win it. Suppose also that we choose a random sample of 20 Colonials games.

Estimate the number of games in the sample that the Colonials win by giving the mean of the relevant distribution (that is, the expectation of the relevant random variable). Do not round your response.

Quantify the uncertainty of your estimate by giving the standard deviation of the distribution. Round your response to at least three decimal places.

a. ___

b. ___

15. A study of college football games shows that the number of holding penalties assessed has a mean of penalties per game and a standard deviation of penalties per game. What is the probability that, for a sample of college games to be played next week, the mean number of holding penalties will be penalties per game or less?

Carry your intermediate computations to at least four decimal places. Round your answer to at least three decimal places.

______

16. Let be a standard normal random variable. Use the calculator provided to determine the value of such that

.

17. The union for a particular industry has determined that the standard deviation of the daily wages of its workers is $ . A random sample of workers in this industry has a mean daily wage of $ . Find a confidence interval for the true mean daily wage of all union workers in the industry. Then complete the table below.

Carry your intermediate computations to at least three decimal places. Round your answers to one decimal place.

What is the lower limit of the 95% confidence interval?

What is the upper limit of the 95% confidence interval?

18. · Consider a *t* distribution with degrees of freedom. Compute . Round your answer to at least three decimal places.

· Consider a *t* distribution with degrees of freedom. Find the value of such that . Round your answer to at least three decimal places.

=

C=

- 19. Suppose that follows a chi-square distribution with degrees of freedom. Compute . Round your answer to at least three decimal places.
- Suppose again that follows a chi-square distribution with degrees of freedom. Find such that . Round your answer to at least two decimal places.
- Find the median of the chi-square distribution with degrees of freedom. Round your answer to at least two decimal places.

P=

K=

Median=

20. The records of a casualty insurance company show that, in the past, its clients have had a mean of auto accidents per day with a standard deviation of . The actuaries of the company claim that the standard deviation of the number of accidents per day is no longer equal to . Suppose that we want to carry out a hypothesis test to see if there is support for the actuaries’ claim. State the null hypothesis and the alternative hypothesis that we would use for this test.

Ho=

H1=

21. A laboratory claims that the mean sodium level, , of a healthy adult is mEq per liter of blood. To test this claim, a random sample of adult patients is evaluated. The mean sodium level for the sample is mEq per liter of blood. It is known that the population standard deviation of adult sodium levels is mEq. Assume that the population is normally distributed. Can we conclude, at the level of significance, that the population mean adult sodium level differs from that claimed by the laboratory?

Perform a two-tailed test. Then fill in the table below.

Carry your intermediate computations to at least three decimal places, and round your responses as specified in the table. (If necessary, consult a list of formulas.)

Ho=

H1=

The type of test statics=Z,T,F OR Chi square

The value=

The two critical values

Can we could the population mean yes or no

22. For a study conducted by the research department of a pharmaceutical company, randomly selected individuals were asked to report the amount of money they spend annually on prescription allergy relief medication. The sample mean was found to be with a standard deviation of . A random sample of individuals was selected independently of the first sample. These individuals reported their annual spending on non-prescription allergy relief medication. The mean of the second sample was found to be with a standard deviation of . As the sample sizes were quite large, it was assumed that the respective population standard deviations of the spending for prescription and non-prescription allergy relief medication could be estimated as the respective sample standard deviation values given above. Construct a confidence interval for the difference between the mean spending on prescription allergy relief medication () and the mean spending on non-prescription allergy relief medication (). Then complete the table below

What is the lower limit 90%

What is the upper limit of 90%