The null and alternate hypotheses are:
A sample of 200 observations from the first population indicated that x1 is 170. A sample of 150 observations from the second population revealed x2 to be 110. Use the .05 significance level to test the hypothesis.
- a. State the decision rule.
- b. Compute the pooled proportion.
- c. Compute the value of the test statistic.
- d. What is your decision regarding the null hypothesis?
Want to see the full answer?
Check out a sample textbook solutionChapter 15 Solutions
EBK STATISTICAL TECHNIQUES IN BUSINESS
- A vending machine company wants to check three of its machines to determine if they are properly dispensing 12 ounces of coffee. Test by using α=0.05. Their data is given below. Machine A Machine B Machine C 11.8 11.7 12.2 12.1 11.9 12.1 12.0 11.7 12.0 11.9 11.8 11.9 12.1 12.0 12.2 Group of answer choices There is sufficient evidence to reject the claim that the proportions are equal because the p-value 0.0255 < 0.05 There is insufficient evidence to conclude the claim that the proportions are equal because the p-value 0.0255 < 0.05 There is insufficient evidence to reject the claim that the proportions are equal because the p-value 0.0255 < 0.05 There is sufficient evidence to conclude the claim that the proportions are equal because the p-value 0.0255 < 0.05arrow_forward13. Consider the following hypothesis test for proportions.H 0: p = 0.30H a: p ≠ 0.30A sample of 500 provided a sample proportion p = 0.285. (a) Find the value of the test statistic (z).(b) With ? = 0.05, what is your conclusion:arrow_forwardA stationery store owner claims that the average price of greeting cards that it has in inventory is less than R25. The null and alternative hypotheses is: A. H0: µ = 25 H1: µ ≠ 25 B. H0: µ > 25 H1: µ < 25 C. H0: µ = 25 H1: µ < 25 D. H0: x ̅ = 25 H1: x ̅ < 25arrow_forward
- As noted on page 275, when the two population means are equal, the estimated standard error for the indepen- dent-measures t test provides a measure of how much difference to expect between two sample means. For each of the following situations, assume that m1 5 m2 and calculate how much difference should be expected between the two sample means. One sample has n 5 6 scores with SS 5 70 and the second sample has n 5 10 scores with SS 5 140. One sample has n 5 6 scores with SS 5 310 and the second sample has n 5 10 scores with SS 5 530. In Part b, the samples have larger variability (big- ger SS values) than in Part a, but the sample sizes are unchanged. How does larger variability affect the magnitude of the standard error for the sample mean difference?arrow_forwardFor each of the following investigations, state i) null hypothesis, ii) alternative hypothesis and iii) type of test, two sided/one sided. a) You wish to investigate if income from tobacco farming is greater than that of from tea farming in Malawi. b) You want to compare proportion of army worms killed by Doom those killed by Attack pesticide.arrow_forwardWhich pair of the hypotheses would be correct for the following claim: Claim: The percentage of cars sold with manual transmission is 2018 (group 1) is lower than the percentage of cars sold with manual transmission in 2010 (group 2) A. H0 :p1 −p2 =0andH1 :p1 −p2 <0 B. H0 :p1 −p2 <0andH1 :p1 −p2 =0 C. H0 :p1 −p2 =0andH1 :p1 −p2 ̸=0 D. H0 :p1 −p2 ̸=0andH1 :p1 −p2 =0 E. H0 :p1 −p2 =0andH1 :p1 −p2 >0 F. H0 :p1 −p2 >0andH1 :p1 −p2 =0arrow_forward
- In a test of H0:p=0.4 against Ha:p≠0.4, a sample of size 100 produces z=1.28 for the value of the test statistic. Thus the p-value of the test is approximately equal to?arrow_forwardAn automobile manufacturer is considering using robots for part of its assembly process. Converting to robots is an expensive process, so it will be undertaken only if there is strong evidence that the proportion of defective installations is less for the robots than for human assemblers. Let p denote the actual proportion of defective installations for the robots. It is known that the proportion of defective installations for human assemblers is 0.02. (a) Which of the following pairs of hypotheses should the manufacturer test? H0: p = 0.02 versus Ha: p < 0.02 or H0: p = 0.02 versus Ha: p > 0.02 Explain your answer. H0: p = 0.02 versus Ha: p < 0.02, as the conversion will only happen if the proportion of defective installations is higher for robots.H0: p = 0.02 versus Ha: p < 0.02, as the conversion will only happen if the proportion of defective installations is lower for robots. H0: p = 0.02 versus Ha: p > 0.02, as the conversion will only happen if the…arrow_forwardA random sample of 1,175 people in a certain country were asked whether they thought climate change was aproblem. The sample proportion of those who think climate change is a problem was calculated, and a 95 percentconfidence interval was constructed as .Which of the following is a correct interpretation of the interval?(A) We are 95 percent confident that any sample of 1,175 people will produce a sample proportion between0.146 and 0.214.(B) We are 95 percent confident that the proportion of all people in the country who think climate change is aproblem is between 0.146 and 0.214.(C) We are 95 percent confident that the proportion of people in the sample who think climate change is aproblem is between 0.146 and 0.214.(D) The probability that 95 percent of all people in the country who think climate change is a problem is between0.146 and 0.214.(E) The probability is 0.95 that the proportion of all people in the country who think climate change is a problemis between 0.146 and 0.214arrow_forward
- For the following pairs of assertions, indicate which do not comply with our rules for setting up hypotheses and why (the subscripts 1 and 2 differentiate between quantities for two different populations or samples):arrow_forwardA vending machine company wants to check three of its machines to determine if they are properly dispensing 12 ounces of coffee. Test by using α=0.01. Their data is given below Machine A Machine B Machine C 11.8 11.7 12.2 12.1 11.9 12.1 12.0 11.7 12.0 11.9 11.8 11.9 12.1 12.0 12.2 A. There is insufficient evidence to conclude the claim that the proportions are equal because the p-value 0.0255 >0.01 B. There is sufficient evidence to reject the claim that the proportions are equal because the p-value 0.0255 > 0.01 C. There is insufficient evidence to reject the claim that the proportions are equal because the p-value 0.0255 > 0.01 D. There is sufficient evidence to conclude the claim that the proportions are equal because the p-value 0.0255 >0.01arrow_forwardA hypothesis test was conducted, at α = 0.05, to determine whether a certain chemical compound lasts longer than 30 seconds under a certain specified condition. The hypotheses used were: H0: µ = 30 Ha: µ > 30 A sample mean of 37.4 seconds was obtained from a sample of size n = 80. All statistical assumptions were met, and a p-value of p = 0.0089 was obtained. Which of the following is correct? a) If the null hypothesis were in reality true that the population mean was equal to 30, then the probability of observing a sample mean of 37.4 seconds from a sample of size n = 80 would be only .0089. b) If the null hypothesis were in reality false that the population mean was equal to 30, then the probability of observing a sample mean of 37.4 seconds (or less) from a sample of size n = 80 would be only .0089. c) If the null hypothesis were in reality true that the population mean was equal to 30, then the probability of observing a sample mean of 37.4 seconds (or greater) from…arrow_forward
- MATLAB: An Introduction with ApplicationsStatisticsISBN:9781119256830Author:Amos GilatPublisher:John Wiley & Sons IncProbability and Statistics for Engineering and th...StatisticsISBN:9781305251809Author:Jay L. DevorePublisher:Cengage LearningStatistics for The Behavioral Sciences (MindTap C...StatisticsISBN:9781305504912Author:Frederick J Gravetter, Larry B. WallnauPublisher:Cengage Learning
- Elementary Statistics: Picturing the World (7th E...StatisticsISBN:9780134683416Author:Ron Larson, Betsy FarberPublisher:PEARSONThe Basic Practice of StatisticsStatisticsISBN:9781319042578Author:David S. Moore, William I. Notz, Michael A. FlignerPublisher:W. H. FreemanIntroduction to the Practice of StatisticsStatisticsISBN:9781319013387Author:David S. Moore, George P. McCabe, Bruce A. CraigPublisher:W. H. Freeman