Test4 review SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.

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1 Provide an appropriate response. ) The dean of a major university claims that the mean time for students to earn a Masterʹs degree is at most.9 years. Write the null and alternative hypotheses. ) ) The mean score for all NBA games during a particular season was less than 0 points per game. State this claim mathematically. Write the null and alternative hypotheses. Identify which hypothesis is the claim. ) ) Given H0: p 80% and Ha: p < 80%, determine whether the hypothesis test is left-tailed, right-tailed, or two-tailed. A) right-tailed B) left-tailed C) two-tailed ) ) A researcher claims that % of voters favor gun control. Determine whether the hypothesis test for this claim is left-tailed, right-tailed, or two-tailed. ) A) left-tailed B) two-tailed C) right-tailed 5) The mean age of bus drivers in Chicago is 5.5 years. Identify the type I and type II errors for the hypothesis test of this claim. 5) ) The mean age of bus drivers in Chicago is 59. years. If a hypothesis test is performed, how should you interpret a decision that fails to reject the null hypothesis? ) A) There is sufficient evidence to support the claim μ= 59.. B) There is sufficient evidence to reject the claim μ = 59.. C) There is not sufficient evidence to support the claim μ = 59.. D) There is not sufficient evidence to reject the claim μ = ) The mean IQ of statistics teachers is greater than 0. If a hypothesis test is performed, how should you interpret a decision that rejects the null hypothesis? 7) A) There is not sufficient evidence to reject the claim μ > 0. B) There is sufficient evidence to reject the claim μ > 0. C) There is sufficient evidence to support the claim μ> 0. D) There is not sufficient evidence to support the claim μ > 0.

2 8) Given H0: μ, for which confidence interval should you reject H0? 8) A) (.5,.5) B) (0, ) C) (, ) 9) Suppose you are using α = 0.05 to test the claim that μ> using a P-value. You are given the sample statistics n = 50, x =., and s =.. Find the P-value. A) 0.08 B) 0.08 C) 0. D) ) 0) Given H0: μ 8 and P = Do you reject or fail to reject H0 at the 0.05 level of significance? 0) A) not sufficient information to decide B) reject H0 C) fail to reject H0 ) A fast food outlet claims that the mean waiting time in line is less than. minutes. A random sample of 0 customers has a mean of. minutes with a standard deviation of 0. minute. If α = 0.05, test the fast food outletʹs claim. ) ) You wish to test the claim that μ > at a level of significance of α = 0.05 and are given sample statistics n = 50, x =., and s =.. Compute the value of the standardized test statistic. Round your answer to two decimal places. A).77 B). C) 0.98 D). ) ) Suppose you want to test the claim that μ 5.. Given a sample size of n = 5 and a level of significance of α = 0.05, when should you reject H0? ) A) Reject H0 if the standardized test statistic is less than -.8. B) Reject H0 if the standardized test statistic is less than.575. C) Reject H0 if the standardized test is less than -.9. D) Reject H0 if the standardized test statistic is less than -.5. ) Find the standardized test statistic t for a sample with n =, x =., s =., and α = 0.0 if H0: μ =. Round your answer to three decimal places. ) A).00 B).890 C). D).99

3 5) A local group claims that the police issue more than 0 speeding tickets a day in their area. To prove their point, they randomly select two weeks. Their research yields the number of tickets issued for each day. The data are listed below. At α = 0.0, test the groupʹs claim using P-values. 5) ) Determine whether the normal sampling distribution can be used. The claim is p < 0.5 and the sample size is n = 8. ) A) Use the normal distribution. B) Do not use the normal distribution. 7) An airline claims that the no-show rate for passengers is less than 5%. In a sample of 0 randomly selected reservations, 9 were no-shows. At α = 0.0, test the airlineʹs claim. 7) 8) Compute the standardized test statistic, X, to test the claim σ =.5 if n =, s = 8, and α = ) A) 9.09 B) 8.90 C).9 D) 0.9 9) A trucking firm suspects that the variance for a certain tire is greater than,000,000. To check the claim, the firm puts 0 of these tires on its trucks and gets a standard deviation of 00 miles. If α = 0.05, test the trucking firmʹs claim using P-values. 9) Identify the explanatory variable and the response variable. 0) An agricultural business wants to determine if the rainfall in inches can be used to predict the yield per acre on a wheat farm. 0) Provide an appropriate response. ) The data below are the gestation periods, in months, of randomly selected animals and their corresponding life spans, in years. Construct a scatter plot for the data. Determine whether there is a positive linear correlation, a negative linear correlation, or no linear correlation. ) Gestation, x Life span, y

4 ) The data below are the number of absences and the final grades of 9 randomly selected students from a statistics class. Calculate the correlation coefficient, r. ) Number of absences, x Final Grade, y A) B) C) D) ) Given a sample with r = -0.75, n =, and α = 0.0, determine the critical values t0 necessary to test the claim ρ = 0. A) ±.58 B) ±.8 C) ±.7 D) ±.080 ) ) Find the equation of the regression line for the given data. ) x y A) y^ =.097x B) y^ = 0.0x C) y^ =.097x D) y^ = -0.0x ) Use the regression equation to predict the value of y for x = -.5. Assume that the variables x and y have a significant correlation. 5) x y A).09 B) -.0 C).58 D) 0.78 ) Find the equation of the regression line by letting Row represent the x-values and Row represent the y-values. Now find the equation of the regression line letting Row represent the x-values and Row represent the y-values. What effect does switching the explanatory and response variables have on the regression line? ) Row Row

5 7) Find the standard error of estimate, se, for the data below, given that y^ =.5x. 7) x y A) 0.75 B) 0.9 C) 0.5 D) 0.8 8) Calculate the coefficient of determination, given that the linear correlation coefficient, r, is What does this tell you about the explained variation and the unexplained variation of the data about the regression line? 8) 9) Construct a 95% prediction interval for y given x =.5, y^ =.5x and se = 0.8. Round interval to three decimal places. 9) x y A) -.5 < y <.5 B) -5.5 < y <.0 C) -8. < y < -.5 D).59 < y < ) A multiple regression equation is y^ = -5, x + 0,000x, where x is a personʹs age, x is the personʹs grade point average in college, and y is the personʹs income. Predict the income for a person who is years old and had a college grade point average of.5. A) $9,0 B) $5,5 C) $5,0 D) $89,0 0) ) The frequency distribution shows the ages for a sample of 00 employees. Find the expected frequencies for each class to determine if the employee ages are normally distributed. ) Class boundaries Frequency, f

6 ) Many track runners believe that they have a better chance of winning if they start in the inside lane that is closest to the field. For the data below, the lane closest to the field is Lane, the next lane is Lane, and so on until the outermost lane, Lane. The data lists the number of wins for track runners in the different starting positions. Calculate the chi-square test statistic χ to test the claim that the number of wins is uniformly distributed across the different starting positions. The results are based on 0 wins. ) Starting Position 5 Number of Wins 5 50 A).59 B) 9. C) 5.5 D).750 ) The frequency distribution shows the ages for a sample of 00 employees. Are the ages of employees normally distributed? Use α = ) Class boundaries Frequency, f

7 Find the marginal frequencies for the given contingency table. ) Blood Type O A B AB Sex F M ) A) B) C) D) Provide an appropriate response. 5) The contingency table below shows the results of a random sample of 00 state representatives that was conducted to see whether their opinions on a bill are related to their party affiliation. 5) Party Republican Democrat Independent Opinion Approve Disapprove No Opinion Find the chi-square test statistic, χ, to test the claim of independence. A) 7. B).75 C) 8.00 D) 9.8 7

8 ) Calculate the test statistic F to test the claim that σ = σ. Two samples are randomly selected ) from populations that are normal. The sample statistics are given below. n = n = s = 0.57 s =.75 A).5 B) C).57 D).0 7) Find the left-tailed and right tailed critical F-values for a two-tailed test. Use the sample statistics below. Let α = ) n = 5 n = s = 5.8 s =.7 8) The weights of a random sample of 5 women between the ages of 5 and had a standard deviation of 8 pounds. The weights of a random sample of women between the ages of 55 and had a standard deviation of pounds. Construct a 95% confidence interval for σ σ, where σ and σ are the variances of the weights of women between 8) the ages 5 and and the weights of women between the ages of 55 and respectively. 9) Find the test statistic F to test the claim that the populations have the same mean. 9) Brand Brand Brand n = 8 n = 8 n = 8 x =.0 x =. x =. s = 0.50 s = 0.0 s = 0.55 A).8 B).0 C).0 D) 0.8 8

9 0) A researcher wishes to determine whether there is a difference in the average age of elementary school, high school, and community college teachers. Teachers are randomly selected. Their ages are recorded below. Find the critical value F0 to test the claim that there is no difference in the average age of each group. Use α = ) Elementary Teachers High School Teachers Community College Teachers A) 5. B) 9. C). D)

10 Answer Key Testname: TEST REVIEW ) H0: μ.9, Ha: μ >.9 ) claim: μ < 0; H0: μ 0, Ha: μ < 0; claim is Ha ) B ) B 5) type I: rejecting H0: μ = 5.5 when μ = 5.5 type II: failing to reject H0: μ = 5.5 when μ 5.5 ) D 7) C 8) C 9) B 0) C ) Fail to reject H0; There is not enough evidence to support the fast food outletʹs claim that the mean waiting time is less than. minutes. ) A ) D ) B 5) P-value = 0.7. Since the P-value is great than α, there is not sufficient evidence to support the the groupʹs claim. ) B 7) critical value z0 =.; standardized test statistic -0.5; fail to reject H0; There is not sufficient evidence to support the airlineʹs claim. 8) A 9) Standardized test statistic ; Therefore, at a degree of freedom of 00, P must be less than P < α, reject H0; There is sufficient evidence to support the firmʹs claim. 0) explanatory variable: rainfall in inches; response variable: yield per acre ) There appears to be a positive linear correlation. ) C ) A ) D 5) C ) The sign of m is unchanged, but the values of m and b change. 7) D 8) The coefficient of determination, r, = 0.9. That is, 9.% of the variation is explained and 0.9% of the variation is unexplained. 9) B 0

11 Answer Key Testname: TEST REVIEW 0) A ),,,, and 7, respectively. ) D ) Critical value χ0 = 9.88; chi-square test statistic χ =.77; fail to reject H0; The ages of employees are normally distributed. ) C 5) C ) A 7) FL = 0.07, FR = 7.9 8) (0.87,.57) 9) C 0) C