Which one of the following graphs represents the rejection region for this test? Only type the letter of the option you choose Rejeet He Reject H Reject Rejeet H
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A clothing store owner wants to determine if offering a 10% discount to all account holders will encourage them to buy more. This offer was made available to 200 clients who spent R1000 or more at the store in the past year. After one year it was found that for this sample of 50 customers on average each customer spent R327,14 more than the previous year with a standard deviation of R489,03. The store owner wants to determine that if he offers discount to all account holders at the store that the average amount that customers spend will be more than R250 at a 1% level of significance.
1.1 Formulate the null and alternative hypothesis by filling in the missing symbols and values. (Image attached)
1.2 which one of the following graphs represents the rejection region for the test ? (Image attached)
1.3 what is the statistic value (round answer to 4 decimal places)
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- A study was conducted to investigate the effect of a new drug on blood pressure. A sample of 25 patients was randomly selected and their blood pressure was measured both before and after taking the drug. The sample mean blood pressure before taking the drug was 120 mmHg and the sample mean blood pressure after taking the drug was 118 mmHg. The sample standard deviation for the blood pressure before taking the drug was 4 mmHg and the sample standard deviation for the blood pressure after taking the drug was 5 mmHg. Test the hypothesis that the average blood pressure after taking the drug is lower than the average blood pressure before taking the drug using a 0.01 level of significance.A prominent medical group claims that the population mean of the surgery durations for all brain tumor patients is 3.69 hours. You are a data analyst for a health insurance company and want to test that claim. To do so, you select a random sample of 32 brain tumor surgery patients, and you record the surgery duration for each. Assume it is known that the population standard deviation of the durations of all brain tumor surgeries is 1.68 hours. Based on your sample, follow the steps below to construct a 99% confidence interval for the population mean of the surgery durations for all brain tumor patients. Then state whether the confidence interval you construct contradicts the medical group's claim. (If necessary, consult a list of formulas.) (a) Click on "Take Sample" to see the results from your random sample of 32 brain tumor patients. (b) (c) Take Sample Sample size: Point estimate: Population standard deviation: Critical value: Compute 0.00 0.00 Number of patients Enter the values…A marketing consultant is hired by a major restaurant chain wishing to investigate the preferences and spending patterns of lunch customers. The CEO of the chain hypothesized that the average customer spends at least $13.50 on lunch. A survey of 25 customers sampled at one of the restaurants found the average lunch bill per customer to be ?¯=$14.50 . Based on previous surveys, the restaurant informs the marketing manager that the standard deviation is ?=$3.50 . To address the CEO’s conjecture, the marketing manager carried out a hypothesis test of ?0:?=13.50 vs. ??:?>13.50 and obtained a ?‑value = 0.77. The marketing chooses a significance level of ?=0.10. If he uses this significance level throughout his work, how often will he reject a true null hypothesis? Group of answer choices a.He will reject 10% of all true null hypotheses. b. He will reject 1% of all true null hypotheses. c. He will reject 5% of all true null hypotheses. d. He will not reject 10% of all true null…
- The owner of a local nightclub has recently surveyed a random sample of n = 250 customers of the club. She would now like to determine whether or not the mean age of her customers is over 30. If so, she plans to alter the entertainment to appeal to an older crowd. If not, no entertainment changes will be made. Suppose she found that the sample mean was 30.45 years and the sample standard deviation was 5 years. What is the p value associated with the test statistic?A new small business wants to know if its current radio advertising is effective. The owners decide to look at the mean number of customers who make a purchase in the store on days immediately following days when the radio ads are played as compared to the mean for those days following days when no radio advertisements are played. They found that for 10 days following no advertisements, the mean was 18.3 purchasing customers with a standard deviation of 1.8 customers. On 7 days following advertising, the mean was 19.4 purchasing customers with a standard deviation of 1.6 customers. Test the claim, at the 0.02 level, that the mean number of customers who make a purchase in the store is lower for days following no advertising compared to days following advertising. Assume that both populations are approximately normal and that the population variances are equal. Let days following no advertisements be Population 1 and let days following advertising be Population 2. Step 3 of 3: Draw a…A pharmaceutical company needs to know if its new cholesterol drug, Praxor, is effective at lowering cholesterol levels. It believes that people who take Praxor will average a greater decrease in cholesterol level than people taking a placebo. After the experiment is complete, the researchers find that the 44 participants in the treatment group lowered their cholesterol levels by a mean of 18.7 points with a standard deviation of 3.3 points. The 39 participants in the control group lowered their cholesterol levels by a mean of 18.1 points with a standard deviation of 2.1 points. Assume that the population variances are not equal and test the company’s claim at the 0.02 level. Let the treatment group be Population 1 and let the control group be Population 2. Step 1 of 3 : State the null and alternative hypotheses for the test. Fill in the blank below. H0: μ1=μ2 Ha : μ1⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯μ2 Step 2 of 3: what is the test statistic Step 3 of 3: draw a conclusion, fail or reject. Is…
- A telemarketing company knows that the daily average sales is 20. A new telemarketer who has just started with the company claims that the target of 20 sales per day is an unreasonably high target. From the 100 telemarketers working for you, you select a random sample of 16 and calculate the mean and the standard deviation of sales for a day to be 18.5 and 3.2 respectively. Is there any validity in the statement made by the new telemarketer? Test at the 5% level of significance.Researchers want to compare the relative effectiveness of two popular diets. They randomly assign each of 400 volunteers to one of two Groups: A & B. There are 200 volunteers in each group. Group A spends 6 months on Diet A. Group B spends 6 months on Diet B. At the beginning of the study, the difference in average weight between the two groups was negligible. After the study, the Group A had lost on average 7.8 pounds with a standard deviation of 13.4 pounds, while the Group B had lost on average 5.3 pounds with a standard deviation of 14.8 pounds. Determine the z-score/test statistic for a two-tailed test with significance level α = 0.05 , accurate to 2 decimal places.In Professor Krugman’s economics course, the correlation between the students’ total scores prior to the final examination and their final‑examination scores is ?=0.5.r=0.5. The pre‑exam totals for all students in the course have mean 280280 and standard deviation 40.40. The final‑exam scores have mean 7575 and standard deviation 8.8. Professor Krugman has lost Julie’s final exam but knows that her total before the exam was 300.300. He decides to predict her final‑exam score from her pre‑exam total. (a) Which of the choices is the least‑squares regression line of final‑exam scores on pre‑exam total scores in this course?
- A pharmaceutical company needs to know if its new cholesterol drug, Praxor, is effective at lowering cholesterol levels. It believes that people who take Praxor will average a greater decrease in cholesterol level than people taking a placebo. After the experiment is complete, the researchers find that the 34 participants in the treatment group lowered their cholesterol levels by a mean of 22.2 points with a standard deviation of 3.4 points. The 42 participants in the control group lowered their cholesterol levels by a mean of 21.2 points with a standard deviation of 1.8 points. Assume that the population variances are not equal and test the company's claim at the 0.10 level. Let the treatment group be Population 1 and let the control group be Population 2. Step 1 of 3: State the null and alternative hypotheses for the test. Fill in the blank below. Ho:₁ = ₂ Ha: M •M₂A new small business wants to know if its current radio advertising is effective. The owners decide to look at the mean number of customers who make a purchase in the store on days immediately following days when the radio ads are played as compared to the mean for those days following days when no radio advertisements are played. They found that for 13 days following no advertisements, the mean was 23.9 purchasing customers with a standard deviation of 1.9 customers. On 6 days following advertising, the mean was 24.7 purchasing customers with a standard deviation of 1.6 customers. Test the claim, at the 0.01 level, that the mean number of customers who make a purchase in the store is lower for days following no advertising compared to days following advertising. Assume that both populations are approximately normal and that the population variances are equal. Let days following no advertisements be Population 1 and let days following advertising be Population 2. Step 3 of 3: Draw a…A recent study found that 61 children who watched a commercial for potato chips featuring a celebrity endorser ate a mean of 39 grams of potato chips as compared to a mean of 28 grams for 51 children who watched a commercial for an alternative food snack. Suppose that the sample standard deviation for the children who watched the celebrity-endorsed commercial was 21.2 grams and the sample standard deviation for the children who watched the alternative food snack commercial was 12.7 grams. What is the test statistic? tSTAT= __________ (Round to two decimal places as needed.)