Dr. Friedman

E-mail:  x.friedman@worldnet.att.net

Review for Final

(1) A school claims that the average reading score of its students is at least 71. Use the following data and assume a normal distribution. Sample average = 68, standard deviation = 8, n = 16. (a) test this claim at a = .05. (b) Construct a two-sided 95% confidence interval estimate of the true (population) average reading score.

(2) A company claims that its soda machines dispense on average exactly 16 ounces of soda. Use the following data: Sample average = 14.6 ounces, standard deviation = 1.8 ounces, n = 81. (a) test this claim at a = .04. (b) Using the above data, construct a two-sided 90% confidence interval estimate of the true mean.

(3) A company claims that no more than 4% of its computers are defective. In a sample of 100 computers, 9 are found to be defective. (a) Should the computer production line be adjusted? test at a = .01. (b) Using the above data, construct a two-sided 92% confidence interval estimate of the true (population) percentage of defective computers.

(4) A company is interested in determining whether the average salary of men and women is different in their company. A sample of men and women results in the following:
Men: average salary = $69,000 Standard deviation = $10,000 n= 60
Women: average salary = $62,000 Standard deviation = $8,000 n = 30
(a) At a = .03, is there a statistically significant difference between salaries of men and women?
(b) Using the above data, construct a two-sided 95% confidence interval for the true difference between salaries of men and women.

(5) A company is interested in determining whether the average life of HP and Epson printers is different. A sample of HP and Epson printers result in the following:
HP: average life = 7 years Standard deviation = 2 years n= 10
Epson: average life = 5.5 years Standard deviation = 2.5 years n =8
At a = .05, is there a statistically significant difference between the longevity of the two brands of printers?

(6) A company is interested in determining whether the defect rates for computer chips made by two companies is different. A sample of computer chips result in the following:
XYZ: 18 defectives in a sample of 100 computer chips
ADC: 42 defectives in a sample of 200 computer chips
At a = .05, is there a statistically significant difference between the defect rate of the two computer chips?

(7) A researcher wishes to determine whether there is a relationship between the number of job offers one receives and years of college education. A sample of 12 individuals was selected with the following results:

SX = 42
SY= 60
SXY = 261
S(X-squared) = 182
S (Y-squared) = 398

(a) Calculate the regression equation and interpret the meaning of the regression coefficients (a and b).
(b) Compute the correlation coefficient, r, and test it for significance at the a =.05 level.
(c) Compute the coefficient of determination (r-squared) and explain its meaning.
(d) Use the regression equation to predict the number of job offers an individual with 8 years of college could expect.

Answers:
(1) (a) t15 = -1.5 p>.05 do not reject H0 (b) 63.7 <--------> 72.3
(2) (a) Z = -7 p<.04 reject H0 (b) 14.27 oz <------> 14.93 oz
(3) (a) Z = 2.56 p<.01 reject H0 (b) 4% <------> 14%
(4) (a) Z = 3.6 p<.03 reject H0 (b) $3,180 <----->$10,820
(5) t16 = 1.42 p>.05 do not reject H0
(6) Z = -.61 p>.05 do not reject H0
(7)(a) Y = -.10 + 1.46X every year of college results in an additional 1.46 job offers. 0 years of college results in -.10 offers.
(b) r = .87 t10 = 5.6 p <.05 the correlation is significant
(c) r-squared = 75.7%. 75.7% of the variation in the number of job offers received is explained by years of college.
(d) -.10 + 1.46(8) = 11.58 job offers