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99 90 90 50 Percent 10 - 99 90 50 Probability Plot of Placebo, Drug, Diff Normal - 95% CI (A) Placebo 0.0 2.5 5.0 7.5 10.0 Diff (C) 10 1 5 99 90 90 50 10 10 1 10 10 (B) Drug Placebo Mean 5.52 StDev 1.917 N 25 AD 0.533 P-Value 0.156 Drug Mean 436 StDev 1.823 N 25 AD 0.479 0.0 2.5 5.0 7.5 10.0 P-Value 0.215 Diff Mean 1.16 StDev 2.511 N 25 AD 0.598 P-Value 0.108 Output 1 Method H₁population mean of Placebo. Hz: population mean of Drug Difference: μ₁- H₂ Equal variances are assumed for this analysis. Output 2 Descriptive Statistics Sample N Mean StDev SE Mean Placebo 25 5.520 1.917 0.383 Drug 25 4.360 1.823 0.365 Descriptive Statistics Sample N Mean StDev SE Mean Placebo 25 5.52 1.92 0.38 Drug 25 4.36 1.82 0.36 Estimation for Paired Difference Mean StDev SE Mean 1.160 2.511 95% Lower Bound for μ_difference 0.502 0.301 Estimation for Difference Difference Pooled StDev 95% Lower Bound for Difference 1.160 1.871 0.272 Test Null hypothesis Alternative hypothesis H₁₁₂ > 0 T-Value DF P-Value 2.19 48 0.017 u_difference: population mean of (Placebo - Drug) Test Null hypothesis Ho: _difference = 0 Alternative hypothesis H₁: _difference > O T-Value P-Value 2.31 0.015

99 90 90 50 Percent 10 - 99 90 50 Probability Plot of Placebo, Drug, Diff Normal - 95% CI (A) Placebo 0.0 2.5 5.0 7.5 10.0 Diff (C) 10 1 5 99 90 90 50 10 10 1 10 10 (B) Drug Placebo Mean 5.52 StDev 1.917 N 25 AD 0.533 P-Value 0.156 Drug Mean 436 StDev 1.823 N 25 AD 0.479 0.0 2.5 5.0 7.5 10.0 P-Value 0.215 Diff Mean 1.16 StDev 2.511 N 25 AD 0.598 P-Value 0.108 Output 1 Method H₁population mean of Placebo. Hz: population mean of Drug Difference: μ₁- H₂ Equal variances are assumed for this analysis. Output 2 Descriptive Statistics Sample N Mean StDev SE Mean Placebo 25 5.520 1.917 0.383 Drug 25 4.360 1.823 0.365 Descriptive Statistics Sample N Mean StDev SE Mean Placebo 25 5.52 1.92 0.38 Drug 25 4.36 1.82 0.36 Estimation for Paired Difference Mean StDev SE Mean 1.160 2.511 95% Lower Bound for μ_difference 0.502 0.301 Estimation for Difference Difference Pooled StDev 95% Lower Bound for Difference 1.160 1.871 0.272 Test Null hypothesis Alternative hypothesis H₁₁₂ > 0 T-Value DF P-Value 2.19 48 0.017 u_difference: population mean of (Placebo - Drug) Test Null hypothesis Ho: _difference = 0 Alternative hypothesis H₁: _difference > O T-Value P-Value 2.31 0.015

Calculus For The Life Sciences
Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter13: Probability And Calculus
Section13.3: Special Probability Density Functions
Problem 16E
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Please note that this question consists of seven parts. Use the MINITAB outputs provided to you to answer the question. Show all your work/explanation. Just giving the answer without adequate explanation work may result in zero for the question. 

A company that manufactures a homeopathic drug claims that it can reduce the time takes to overcome jet lag from long distance flights. A researcher is interested in testing this claim.

He takes a random sample of 50 passengers making a trip from Las Vegas to Melbourne, Australia. He randomly assigns half of his sample to take the placebo and the remaining half to take the actual drug. 

Then he collected the data on the number of days it took for them to recover from the jet lag from the trip.

Part of the data with some summary statistics is displayed below. Please note that some information may or may not be relevant. 

  Placebo Drug Diff
  4 5 -1
  7 3 4
  6 8 -2
  . . .
  . . .
  9 7 2
  4 1 3
Mean 5.52 4.36 1.16
SD 1.917 1.823 2.511
  1. Are the two samples: Placebo and Drug, independent or dependent? Explain your answer
  2. From the provided plots: (A), (B) and (C), clearly state which plot/plots you would use to check any assumptions.
  3. Do you see any serious violations of those assumptions? Explain your answer without simply saying yes or no.
  4. Researcher is interested in testing the claim made by the company manufacturing the drug. To answer this question, which output: output 1 or output 2 would you use? 
    Output 1 Output 2
       
  5. Explain the reason for your choice of output in part 4.
  6. What is the p value for the test ? Write the probability statement for the p value for this test, and copy the numerical value of the p value from your choice of output.
  7. Using the p value you derived in part 6, what would be your conclusion to the researchers question at 5% significance level (write the conclusion in the context of the problem). 
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99 90 90 50 Percent 10 - 99 90 50 Probability Plot of Placebo, Drug, Diff Normal - 95% CI (A) Placebo 0.0 2.5 5.0 7.5 10.0 Diff (C) 10 1 5 99 90 90 50 10 10 1 10 10 (B) Drug Placebo Mean 5.52 StDev 1.917 N 25 AD 0.533 P-Value 0.156 Drug Mean 436 StDev 1.823 N 25 AD 0.479 0.0 2.5 5.0 7.5 10.0 P-Value 0.215 Diff Mean 1.16 StDev 2.511 N 25 AD 0.598 P-Value 0.108
Transcribed Image Text:99 90 90 50 Percent 10 - 99 90 50 Probability Plot of Placebo, Drug, Diff Normal - 95% CI (A) Placebo 0.0 2.5 5.0 7.5 10.0 Diff (C) 10 1 5 99 90 90 50 10 10 1 10 10 (B) Drug Placebo Mean 5.52 StDev 1.917 N 25 AD 0.533 P-Value 0.156 Drug Mean 436 StDev 1.823 N 25 AD 0.479 0.0 2.5 5.0 7.5 10.0 P-Value 0.215 Diff Mean 1.16 StDev 2.511 N 25 AD 0.598 P-Value 0.108
Output 1 Method H₁population mean of Placebo. Hz: population mean of Drug Difference: μ₁- H₂ Equal variances are assumed for this analysis. Output 2 Descriptive Statistics Sample N Mean StDev SE Mean Placebo 25 5.520 1.917 0.383 Drug 25 4.360 1.823 0.365 Descriptive Statistics Sample N Mean StDev SE Mean Placebo 25 5.52 1.92 0.38 Drug 25 4.36 1.82 0.36 Estimation for Paired Difference Mean StDev SE Mean 1.160 2.511 95% Lower Bound for μ_difference 0.502 0.301 Estimation for Difference Difference Pooled StDev 95% Lower Bound for Difference 1.160 1.871 0.272 Test Null hypothesis Alternative hypothesis H₁₁₂ > 0 T-Value DF P-Value 2.19 48 0.017 u_difference: population mean of (Placebo - Drug) Test Null hypothesis Ho: _difference = 0 Alternative hypothesis H₁: _difference > O T-Value P-Value 2.31 0.015
Transcribed Image Text:Output 1 Method H₁population mean of Placebo. Hz: population mean of Drug Difference: μ₁- H₂ Equal variances are assumed for this analysis. Output 2 Descriptive Statistics Sample N Mean StDev SE Mean Placebo 25 5.520 1.917 0.383 Drug 25 4.360 1.823 0.365 Descriptive Statistics Sample N Mean StDev SE Mean Placebo 25 5.52 1.92 0.38 Drug 25 4.36 1.82 0.36 Estimation for Paired Difference Mean StDev SE Mean 1.160 2.511 95% Lower Bound for μ_difference 0.502 0.301 Estimation for Difference Difference Pooled StDev 95% Lower Bound for Difference 1.160 1.871 0.272 Test Null hypothesis Alternative hypothesis H₁₁₂ > 0 T-Value DF P-Value 2.19 48 0.017 u_difference: population mean of (Placebo - Drug) Test Null hypothesis Ho: _difference = 0 Alternative hypothesis H₁: _difference > O T-Value P-Value 2.31 0.015
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