Question 4 (10 total marks; 2 marks each) Starbucks wants to compare the average amount of time people spent drinking coffee indoors versus outdoors as part of their market research. A random sample of 25 outdoor coffee drinkers spent an average of 14.6 minutes drinking coffee with a sample standard deviation of 5.8 minutes. A random sample of 27 indoor coffee drinkers spent an average of 11.5 minutes drinking coffee with a sample standard deviation of 4.9 minutes. Perform a hypothesis test using $\alpha$ = 0.05 to determine if the average time people spent drinking coffee outdoors is more than the average time people spent drinking coffee indoors. a. State the hypotheses. b. Find the test statistic (round to 4 decimals) c. Use the critical value method to test the hypothesis. d. Use the p-value method to test the hypothesis. e. Is there sufficient evidence to support the claim? State your conclusion in the context of the problem.
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Step 1: Let $\mu_1$ be the average time people spend drinking coffee outdoors and $\mu_2$ be the average time people spend drinking coffee indoors. Show more…
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2. A group of researchers studied wait times for customers at a coffee shop. For a random sample of 145 male customers, the mean wait time was 85.2 seconds with a standard deviation of 50 seconds. For a random sample of 141 female customers, the mean wait time was 113.7 seconds with a standard deviation of 75 seconds. Suppose you would like to determine if the mean wait time for males and females is different. (a) (4 points) Write the null and alternative hypotheses you intend to test. (b) (4 points) List all conditions that must be satisfied in order to use the appropriate testing procedure and indicate whether or not they are satisfied by the sample. (c) (3 points) Compute the test statistic based on the sample data. (d) (3 points) Compute the P-value based on the sample data. (e) (2 points) Should you reject or fail to reject the null hypothesis at the α = 0.05 significance level? (f) (2 points) What does your conclusion tell you about mean wait times for males and females at this coffee shop?
Adi S.
A coffee shop relocates to Italy and wants to make sure that all lattes are consistent. They believe that each latte has an average of 4 oz of espresso. If this is not the case, they must increase or decrease the amount. A random sample of 25 lattes shows a mean of 4.6 oz of espresso and a standard deviation of .22 oz. Use alpha = .05 and run a one sample t-test to compare with the known population mean. a)Hypothesis: H₀: H₁: b) Draw the location of Critical Value, identify the distribution it comes from and the alpha value associated with it. Distribution Critical Value C) Calculate the Test Statistic. Identify the formula in which you use. And find the number. Test Statistic Value D) Conclude your problem in a sentence that fully explains the result of your hypotheses test. Null Hypothesis: Reject or Accept?
Qudsiya A.
Question 3 (a) In studying the amount of time that students of Institution X spend on part-time job per week, a random sample of 25 students is taken and their mean and standard deviation are 125 minutes and 20 minutes, respectively. Construct a 95% confidence interval for the mean amount of time for all students of Institution X spend on part-time job per week. State your assumption(s) and / or approximation(s). [8 marks] (b) Suppose the amount of time spent by retired people watching TV per day is approximately normally distributed with a mean of 6 hours and a standard deviation of 1.5 hours. What is the probability that the average number of hours spent watching TV per day by a random sample of 5 retired people is more than 7 hours? [5 marks] (c) A market research analyst has randomly selected 140 customers and 42 of them can identify the brand of a laundry detergent based on the shape of container. Construct a 95% confidence interval for the population proportion of customers who can identify the brand of laundry detergent based on the shape of container. [4 marks]
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