Question

please use EXCEL preferably

NAME: 1of 1 Solve the following problems and answer the following questions. Justify your solutions and answers with verbal and/or quantitative explanations in order to receive full credit. Even if working as a group, each group member must still submit her or his own copy of the solutions as documentation. Using appropriate technology to expedite these calculations is expected; however, such work must be fully documented or explained. Software printouts or spreadsheet copies should include your name within the text so to verify the work as your own. For Problems #1 through #9, consider the following informtion: The marketing office of the coffee house chain, Cafe Ole, claims that its lower caffeine drip brewed house blend of Arabica coffee beans contains only 75 mg per six-ounce cup. A public health advocacy bureau randomly sampled 36 of these cups of coffee, and found a sample m size cups. The population range for caffeine in lower caffeine coffee is known to be 12 mg. At the 2.5% level of significance, does the average amount of caffeine seem to exceed the coffee house chain's claim? ICOMMENTS&HINTS: Consider a standard Range Rule, as discussed in course handouts and/or during class, to estimate adequately the population standard deviation, so to employ large sample methods. Be sure to interpret the value of alpha properly.] mean of 76 mg of caffeine in the same #1 : What are the null and alternative hypotheses, properly and completely stated? #2: What type of hypothesis test is involved: two-tail, one-tail left, or one-tail right? Explain. #3: Which type of test statistic is generated (ie, z or 1) and why? Explain. #4: Determine the critical value(s) that designate the rejection region(s). Indicate the critical value(s) on an appropriate probability curve (i.e., zor t) so to represent the test in graph form. #5: Determine the test statistic (ie, z or t). #6: Determine the p-value that corresponds to the test statistic. #7: Concisely state the conclusion using appropriate and complete statistical language. #8: Interpret the findings in complete thoughts phrases and within the context of the problem. #9: Use confidence interval methods to affirm your conclusion. Scoring Rubric ## | Con #1 #2 | Ade #3 | A #4 | Ade #51 Adequate, accurate solution, complete and correct #6 #7 #8 | A #9 TOTAL alues 2.5 points 2.0 points 2.0 2.5 2.5 2.5 2.0 2.0 2.0 points ts. Credit | Adequate, accurate solution accurate solution accurate solution accurate solution lete and correct lete and correct lete and correct e and corect | Adequate, accurate solution | Adequate, accurate solution accurate solution Adequate, accurate solution e and correct and correct and correct e and correct

Answer 1

#1. Null hypothesis : The average amount of caffeine in the house brewed blend of arabica is less than or equal to 75 mg

Alternate hypothesis: The average amount of caffeine in the house brewed blend of arabica is greater than 75 mg

#2. The type of test involved is "one-tailed right" since the region of rejection must fall under the upper tail to show the probability that the caffeine sampled falls greater than the amount claimed by the manufacturer.

#3. A Z test is used here since the population Range is known via which the population standard deviation can be found out. Also the sample size is greater than 30.

#4. The critical rejection region at 2.5% level of significance is 1.96 is also shown below

25% -1 1 Standard Deviations -3 -2 2 3 Z 1.96

#5. Test statistic = Z = (Sample mean - mean under null hypothesis) / (standard deviation/sqrt(sample size))

Rule of thumb is standard deviation = range / 4 = 12/4 = 3

Z = (76 - 75) / (3/sqrt(36)) = 1/3 = 0.944

#6. The p-value corresponding to the test statistic = 0.173

#7. Since the pvalue is not greater than 0.025, we conclude that "we fail to reject the null hypothesis" i.e. "we fail to reject the claim that the amount of caffeine in the house brewed blend of arabica is less than or equal to 75 mg"

#8.

#9.