Telemarketers obtain names and telephone numbers from several sources. To determine whether one particular source is better than a second, random samples of 400 and 420 names and numbers were obtained from sources A and B, respectively of which 52 and 46 from A and B made a purchase. Construct a 99% confidence interval for PA PB, the difference in the proportions of customers making a purchase from the two sources.
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- Suppose you work as a manager for a large clothing store. You are considering introducing a loyalty program to encourage customers to spend more at your store. Before rolling out your program to the public, you want to do a small experiment to estimate its effectiveness. You offer the loyalty program to 10 random customers, and also observed the sales of 27 random customers who did not get the program as a control group. The customers that were part of the loyalty program had average monthly sales of $302.57 and a sample standard deviation of $49.73. For the control group, the customers had an average monthly sales of $231.65 and a sample standard deviation of $67.88. * Given a 95% confidence interval critical value of t = 2.04, what is the upper bound (upper end) of a 95% confidence interval for the difference between two averages? Use (μloyalty program no loyalty program) for the order. Note: 1- Only round your final answer. Round your final answer to two decimal places.A researcher conducts an independent-measures study to examine how the brain chemical serotonin is related to aggression. One sample of rats serves as a control group and receives a placebo that does not affect normal levels of serotonin. A second sample of rats, low serotonin group, receives a drug that lowers brain levels of serotonin. Then, the researcher tests the animals by recording the number of aggressive responses each of the rats display. See the data below. Is there a significant difference between the control group and the low serotonin group regarding the number of aggressive responses? Control Low Serotonin n = 10 n = 15 M = 14 M = 19 SS = 180.5 SS = 130 Perform a hypothesis test using independent-measures t-test. Use a two-tailed…The College Board provided comparisons of Scholastic Aptitude Test (SAT) scores based on the highest level of education attained by the test taker's parents. A research hypothesis was that students whose parents had attained a higher level of education would on average score higher on the SAT. The overall mean SAT math score was 514. SAT math scores for independent samples of students follow. The first sample shows the SAT math test scores for students whose parents are college graduates with a bachelor's degree. The second sample shows the SAT math test scores for students whose parents are high school graduates but do not have a college degree. College Grads 485 487 518 517 650 542 570 426 566 499 588 562 497 448 592 453 High School Grads 442 492 580 478 479 425 486 485 528 390 524 535 (b) What is the point estimate of the difference between the means for the two populations? (c) Find the value of the test statistic. (Round your answer…
- The College Board provided comparisons of Scholastic Aptitude Test (SAT) scores based on the highest level of education attained by the test taker's parents. A research hypothesis was that students whose parents had attained a higher level of education would on average score higher on the SAT. The overall mean SAT math score was 514. SAT math scores for independent samples of students follow. The first sample shows the SAT math test scores for students whose parents are college graduates with a bachelor's degree. The second sample shows the SAT math test scores for students whose parents are high school graduates but do not have a college degree. High School Grads College Grads 501 487 550 634 538 550 572 497 533 526 394 531 594 432 608 485 442 580 479 486 528 524 492 478 425 485 390 535In the NFL, Coaches can throw "challenge" flags if they believe officials have made an incorrect call on the field. Then, based upon further analysis, the call is either overturned (because the referees were incorrect) or upheld (referees were correct). In the first eight weeks of last NFL season, there were 316 challenges made, with 154 of those calls overturned. The NFL team owners used this data to begin a lawsuit that claimed referees were wrong more than 50% of the time in challenged situations. They want to perform statistical analysis before filing that lawsuit. For the following question, select the answer which correctly responds. 0.50Researchers asked soda drinkers to view either the logo for their favorite soda or a graphic warning demonstrating the harmful effects of sugary beverages (e.g., tooth decay, obesity) and then measured their negative mood with a short survey. They found that those participants who saw the warnings reported significantly greater negative moods than those who saw the logos. Which statistical test should be used?
- A study was done to determine if food insecurity/hunger impacts psychological distress (this is fake data to make it simple, but it is based off of a 2020 study that examined the associations between food insecurity and psychological distress among older people in Ghana). Participants were broken into three groups based on their responses: no food insecurity, moderate food insecurity, and severe food insecurity. Psychological distress was measured on the Kessler Psychological Distress Scale (K10), where scores range from 0 to 50. Enter data and test to determine if there is a significant difference between the 3 groups in psychological distress Food insecurity: Psychological distress scores (higher = more distress) No food insecurity 5 6 8 10 5 4 14 9 Moderate food insecurity 16 14 9 7 14 8 16 17 Severe food insecurity…A statistics content developer at Aplia wanted to know whether study skills are related to memory quality. She invited student volunteers to perform an online memory task. The students saw a list of 60 words and were then asked to recognize a list of 10 words that were on the original list. Students were also asked to provide their GPAs. Consider the following data set, which was collected from student volunteers in 2009. The table gives the frequency for five intervals of scores on the number of correctly identified words. Use the dropdown menus to complete the table by filling in the missing values for the proportions and percentages. Score Interval f Proportion Percentage 9–10 29 0.19 19% 7–8 53 5–6 50 3–4 22 0.14 14% 1–2 1 0.01 1%The U.S. National Center for Health Statistics complies birth statistics and publishes the results in vital statistics of the United States. The Center has historically believed that the mean of all newborns in the U.S. has been no less than 6.95 pounds. A sample of babies is selected so that the center can revise its belief. The following birth weights, in pounds are recorded: 7.4, 6.0, 8.6, 4.5, 2.0, 7.9, 4.0, 2.6, 5.9, 7.3, 7.3, 7.0, 6.3, 8.1, 7.1, 7.3, 6.6, 5.2, 9.8, 8.0, 10.9, 6.5, 3.8, 5.0, 8.0 a). At 5% level of significance, do these data provide sufficient evidence to refute the Center’s belief? Your conclusion must be in terms of the P-Value as well as setting up a Rejection Region. You must show all necessary work. b). Which statistical distribution should be applied in this situation and why? Explain carefully.
