**Understanding Statistical Testing in Supermarket Customer Studies****Context:**Executives of a supermarket chain are evaluating the duration of shopping trips, which is typically reported to be 38 minutes. They suspect this time might differ, prompting a statistical analysis by a consultant, who collects a random sample. The consultant identifies that the mean of the sample is 34 minutes, with a standard deviation of 12 minutes. **Hypothesis Testing:**(a) **Formulating Hypotheses:**- **Null Hypothesis (H₀):** μ = 38- **Alternative Hypothesis (H₁):** μ < 38(b) **Type of Error When Rejecting Null Hypothesis:**If the consultant rejects the null hypothesis, she might make a **Type I error**.(c) **Understanding Type I Error:**Should the true mean shopping time be 38 minutes, a Type I error would involve:- Failing to reject the hypothesis that μ is less than 38 when, in fact, μ is equal to 38.**Diagram:** The image includes an interface where responses are input directly on corresponding fields, with adjustments made via dropdown menus.This exercise emphasizes the importance of hypothesis formulation and error types in statistical methods, vital for accurate business insights.

Answered: Executives of a supermarket chain are…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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Similar questions

What price do farmers get for their watermelon crops? In the third week of July, a random sample of 40 farming regions gave a sample mean of x = $6.88 per 100 pounds of watermelon. Assume that ? is known to be $1.92 per 100 pounds.
A cruise ship charges passengers $3 for a can of soda. Because of passenger complaints, the ship manager has decided to try out a plan with a lower price. He thinks that with a lower price, more cans will be sold, which would mean that the ship would still make a reasonable total profit. With the old pricing, the mean number of cans sold per passenger for a 10-day trip was 10.3 cans. Suppose μ represents the mean number of cans per passenger for the new pricing. What hypotheses should the ship manager test if he wants to determine if the mean number of cans sold is greater for the new pricing plan? O Ho: μ = 10.3 versus H₂: μ> 10.3 O Ho: μ = O Ho: μ = 10 versus Ha: μ 10.3
Warren wants to know if the amount of coffee that you drink is related to the number of hours that you stay awake. He recruits 50 participants using random sampling to report how much coffee they drank and the time of the day that they went to sleep. He then performs a correlation to determine the association between the amount of coffee that was consumed and the number of hours that they stayed awake. There was a statistically significant positive correlation between amount of coffee that participants drank and the number of hours that they stayed awake, r(49) = .82, p < .05, two-tailed, r2 = .08. This was a small effect – 8% of the variance in the amount of coffee drank is explained by hours that you stay awake (and vice versa).
Justin wants to know whether a commonly prescribed drug does improve the attention span of students with attention deficit disorder (ADD). He knows that the mean attention span for students with ADD who are not taking the drug is 2.3 minutes long. His sample of 12 students taking the drug yielded a mean of 4.6 minutes. Justin can find no information regarding σx , so he calculated s2x =1.96. a. Identify the independent and dependent variables. b. In a sentence, state the null hypothesis being tested. c. Using symbols, state the null and alternative hypotheses. d. Determine the critical region using a one-tailed test with alpha = .05. e .Conduct the hypothesis test (Do the math and compare the t-critical and t-obtained values). f. State your conclusions in terms of H0 (Should you reject the H0 or fail to reject/accept the H0). g. Based on your analysis, is there a relationship between the drug and attention span?
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A physical therapist wanted to know whether the mean step pulse of men was less than the mean step pulse of women. She randomly selected 59 men and 73 women to participate in the study. Each subject was required to step up and down a 6-inch platform. The pulse of each subject was then recorded. The following results were obtained. SE Mean 1.5 1.7 SIDev 11.2 Mean 112.7 Men Women 99% CI for mu Men - mu Women -11.89, 0.09) T-Test mu Men mu Women (vs<) T= -2.61 P=0.0051 DF 129 59 73 118.6 14.8 Two sample T for Men vs Women State the researcher's condlusion. Which of the following is correct? O A Reject Ha, there is sufficient evidence to condlude that the mean step pulse of men was less than the mean step pulse of women the mean step pulse of women O B. Reject Ha, there is not sufficient evidence to condlude that the mean step pulse of men was less OC. Fail to reject Ho, there is sufficient evidence to conclude that the mean step pulse of men was less than the mean steg pulse of women O D.…
Clara and Rose work at different companies. Clara earns an annual salary of 55,500 and Rose earns an annual salary of 58,000, but they are curious to know whose salary is closer to the mean salary at her company. Clara calculates a z-score of z=−0.45 for her salary, when compared to her company, and Rose calculates a z-score of z=−0.33. Whose salary is closer to the mean salary at her company? Select the correct answer below:
A psychology student conducted a study on using a chief executive officer's facial structure to predict a firm's financial performance. The facial width-to-height ratio (WHR) for each in a sample of 55 CEOs at publicly traded firms was determined. The sample resulted in x=1.74 and s=2.02. The student wants to predict the financial performance of a firm based on the value of the true mean facial WHR of CEOs. The student wants to use the value of μ=2.3. Do you recommend he use this value? Conduct a test of hypothesis for μ to help you answer the question. Specify all the elements of the test, including H0, Ha, test statistic, p-value, and your conclusion. Test at α=0.10. Find the p-value. p-value=enter your response here (

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