Elementary Statistics Final

Math 160 Final Exam practice for chapters 7 -10 1) True / False

A) The value of the χ2 random variable can be negative. _____________

B) The correlation coefficient r measures the strength of a linear relationship._______

C) α represents the probability of making a type I error ( rejecting the null

hypothesis when it’s actually true) ___________ A study was conducted to determine whether magnets are effective at treating back pain. One group was given the magnet treatment, while the other group was given the sham treatment. The results are shown below where measurements are centimeters on a pain scale. Do not assume the population standard deviations are equal. Magnet:

n1 = 23, x1 = 0.47, s1 = 0.95 Sham: (similar to a placebo)

n2 = 25, x2 = 0.32, s2 = 1.45

2) Construct a 95% confidence interval for the difference between the two population

means. Round to the thousandths place. 3) Based on the results, does it appear that the two populations have different means?

EXPLAIN your answer using the interval from the previous answer.

Quarters are currently minted with weights having a mean of 5.977 and a standard deviation of 0.069. New equipment is being tested in an attempt to improve quality by reducing variation. A simple random sample of 25 quarters is obtained from those manufactured with the new equipment, and this sample has a standard deviation of 0.042. Use a 0.05 significance level to test the claim that quarters manufactured with the new equipment have weights with a standard deviation less than 0.069 4) What is the null hypothesis? ____________ 5) What is the alternate hypothesis?____________ 6) Find the test statistic 7) The critical value is 8) Which is the correct conclusion for the problem. _________

a) The sample data support the claim that quarters manufactured with the new equipment have weights with a standard deviation less than 0.069

b) There is not sufficient sample evidence to support the claim that quarters manufactured with the new equipment have weights with a standard deviation less than 0.069

c) There is sufficient evidence to warrant rejection of the claim that quarters manufactured with the new equipment have weights with a standard deviation less than 0.069

d) There is not sufficient evidence to warrant rejection of the claim that quarters manufactured with the new equipment have weights with a standard deviation less than 0.069

Does the new equipment appear to be effective in reducing the variation of weights? Yes/No

A social worker is interested in looking at the average daily calorie intake from children in the inner city. A sample of six children is taken, and the following results were obtained: 1125, 1019, 1954, 1546, 1418, 980 9) Construct a 99% confidence interval estimate of the mean daily caloric intake for all

inner city children. Round your answer to the tenths place.

10) A recent poll reported that 27% of respondents carrying heavy mortgage or credit

card debt also said that they had stomach ulcers. Find the sample size needed to estimate the population proportion of respondents carrying heavy debt who also have stomach ulcers. We want to be 95% confident that the estimate is within 1 percentage point of the true proportion.

A researcher claims that listening to Mozart improves scores on math quizzes. A random sample of five students took math quizzes, first before and then after listening to Mozart. Test the claim that listening to Mozart improves scores on math quizzes. Use a .01 significance level. Before 75 50 80 85 95 After 85 45 85 95 95 11) The null hypothesis is _____________ 12) The alternate hypothesis is ______________ 13) The test statistic is _______________ 14) The p-value is ______________ 15) Choose one. a) FAIL TO REJECT 0H b) REJECT 0H . 16) Does listening to Mozart improve scores on math quizzes? Yes / No

A study compared the body weight and brain weight for a random sample of mammals. We are interested in estimating brain weight based on body weight. Body Weight (x) (kilograms)

52.16 60 27.66 85 36.33 100 35 62

Brain Weight (y) (grams)

440 81 115 325 119.5 157 56 1320

Round to the thousandths place 17) Find the value of the linear correlation coefficient (r) 18) Is there a significant linear correlation? ( This is not just a “yes” or “no” question,

show all steps in a hypothesis test leading to your answer) 19) If a significant linear correlation exists, find the regression equation. If there is no

significant linear correlation, find y . 20) Find the best predicted brain weight for a mammal with a body weight of 83 kg.

KEY: 1) a) False b) True c) True 2) − 0.559 < µ1 − µ2 < 0.859 3) Since the confidence interval contains zero then it is possible for µ1 − µ2 = 0 if this is the case then µ1 = µ2 and we conclude that there is no difference between the two populations. 4) H0 :σ = .069 5) H1 :σ < .069 (claim) 6) χ 2 = 8.892 7) critical valueis χL

2 = 13.848 reject H0 since test statistic falls in critical region. 8) A / Yes

9) 722.5 < µ < 1958.2 (using T - interval) 10) n = 7572 11) H0 : µd = 0 12) H1 : µd < 0 (claim) 13) t = −1.372 14) p −valueis 0.1210 since this is greater than the significance level α reject H0 15) A 16) NO

17) r = .171 (STAT -> calc -> LinReg L1,L2) 18) 2 methods here − H0 : ρ = 0 (no significant linear correlation) H1 : ρ ≠ 0 (significant linear correaltion) Test Statistic r = .171 Critical Value is + / − 0.707 since test statistic is less than the absolute value of the critical value. Fail to reject H0 so there is no significant linear correlation. 19) Since there is no significant linear correlation use y for predictions. y= 326.69 20) 326.69 (the mean is the best predictor since there is no significant linear correlation. Do not use the regression equation for predictions.)