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STATS Lab Activity 07 Assignment




Question;Hypothesis Testing ? Proportion and One MeanP-value Guidelines when using Standard Normal Table (i.e. the Z-table):Keep this in mind: The method for finding the p-value is based on the alternative hypothesis.Minitab will provide the p-value but if doing by hand using Table A1 observe the following:For Ha: p? po then the p-value = 2P(Z? |z|) That is, find 1 ? P(Z po then the p-value = P(Z? z)For Ha: p 1 proportion, click Summarized Data, enter 2000 fornumber of trials and 1050 for Number of events. Click on Options, AND enter 0.5 where it says?Test proportion.? Click on Options button. Use the default 95.0 for ?Confidence level.? Selectthe alternative hypothesis as ?Proportion Basic Stats > 1 proportion, click Summarized Data, enter 80 fornumber of trials and 7 for Number of events. Click on Perform Hypothesis Test and enter 0.1where it says ?Hypothesized proportion? AND click Options to select the alternative hypothesisas ?smaller than? AND also click on ?Normal approximation? for Method.SPSS Users: Open the Excel Summarized Procedures and select the tab ?Z test of a Proportion?. Enter0.0875 as the Sample Proportion, 80 for the Sample Size, and 0.1 for the Hypothesized Proportion.NOTE: The resulting p-value is for a two-sided test (i.e. ?not equal? alternative hypothesis ? if you areconducting a one-sided test, where your alternative is specified as either ?less than? or ?greater than? youwill need to cut this p-value in half to arrive at the proper p-value for the one-sided test).What value is given for Z in the output?What is the p-value?i. Do the Z test statistic you found by hand in part c and the p-value from part dapproximately equal to the Z statistic found in part e when using Minitab?ii. Decide whether the result is significant based on the p-value from Minitab and report aconclusion in the context of this situation.iii What would the p-value have been if the study wanted to test if a decaffeinated coffeedrinkers are exactly 10% of the coffee drinker population? That is, test Ho: p = 0.1 versus Ha: p? 0.13 A financial analyst wanted answer a fundamental question faced with any investor: doesinvesting in S&P 500 stock index provide long-term return that is beyond the inflation rate? Theanalyst collected monthly total return data of S&P 500 Index since 1950. She also estimated thatthe average monthly inflation rate based on the Consumer Price Index (CPI) is 0.21%. Use theSPXMonthlyData file to test whether the S&P 500 monthly return is larger than averagemonthly inflation rate of 0.21%. Perform hypothesis testing first by hand and then with Minitab.The descriptive statistics are: sample size is 776, sample mean is 0.61%, and the sample standarddeviation is 4.185 %.a. Write the null and alternative hypotheses using appropriate statistical notation.H0:Ha:b. Calculate DF, the t-statistic, and 95% confidence interval:DF == (0.61% - 0.21%) / (4.185% / sqrt(775)) =c. From T-Table what is the range of the p-value based on you t-statistic? NOTE: if you selecteda two-sided Ha (i.e. used?) then you need to double the p-values found in the table.d. Based on your p-value what is your decision and conclusion?e. Now use Minitab to verify your results. Go to Stat > Basic Statistics > 1-Sample t and selectReturn (column C8). Click the box for ?Perform Hypothesis Test? and enter the value from yourhypotheses statements (i.e. uo). Click on Options and select the correct alternative. Click OKtwice and copy and paste your Minitab results. Do your results by hand and those from Minitabroughly match?


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