STAT+008+Lab+%2313

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008

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Statistics

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Apr 3, 2024

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STAT 008 | Lab #13 Page 1 of 6 STAT 008 AFlores 11.21 Goal: Calculating p-values and critical values for hypothesis tests. Using Excel to perform a hypothesis test using all three approaches. Required: Lecture notes, calculator, Standard Normal table, and Excel Hypotheses Assumption Test Statistic Confidence Interval 0 : o H µ µ = versus 0 0 0 : : : a a a H H H µ µ µ µ µ µ ≠ < > Normal distribution σ known 0 x z n µ σ − = 2 x z n α σ   ±     Part I: Finding p-values Consider the following hypothesis tests. Use the standard normal table to find the p-value for the specified alternative hypothesis and test statistic. Show all work, including completing the sketch. Write your final answer in the box provided. 1) Ha: µ > µ 0 (σ known) with t.s. = 1.23 2) Ha: µ < µ 0 (σ known) with t.s. = -2.15 3) Ha: µ ≠ µ 0 (σ known) with t.s. = -2.76 p- value = p- value = p- value =

STAT 008 | Lab #13 Page 2 of 6 STAT 008 AFlores 11.21 4) Ha: µ > µ 0 (σ known) with t.s. = 5.19 Part II: Finding Critical Values Consider the following hypothesis tests. Use the standard normal table to find the critical value for the specified alternative hypothesis and level of significance. Show all work, including completing the sketch. Write your final answer in the box provided. 5) Ha: µ > µ 0 (σ known) with α = 0.05 6) Ha: µ ≠ µ 0 (σ known) with α = 0.05 7) Ha: µ < µ 0 (σ known) with α = 0.01 8) Ha: µ ≠ µ 0 (σ known) with α = 0.10 Critical Value = Critical Value = Critical Value = Critical Value = p- value =

STAT 008 | Lab #13 Page 3 of 6 STAT 008 AFlores 11.21 Part III: Hypothesis Testing Confidence Interval Approach Construct a (1- α)100% confidence interval to estimate the parameter of interest. Use it to perform a hypothesis test. Many bank employees are paid by the hour. Consider a small bank called BBBanking which is currently hiring. During the interviewing process, BBBanking’s manager indicates that it pays its hourly tellers comparable to any other bank. To ensure he is making an accurate statement, he collects a random sample of full-time hourly tellers’ wages. Here are their wages (in dollars per year). 21,985 17,531 17,254 18,575 20,688 18,082 17,392 19,282 19,114 18,418 19,077 19,626 22,753 16,750 Suppose the wages are normally distributed with standard deviation $2000. In addition, it is known that other banks pay their tellers an average of $20,000 per year. Use Excel to find the following (enter the data in column A). x = ______________ 0 µ = ______________ X σ = ______________ n = _______ Construct a 95% CI to estimate the true average wage for BBBanking’s full-time hourly tellers. NOTE: Excel can be used to find the MOE using the formula = CONFIDENCE.NORM(α, σ, n ) Perform a hypothesis test to determine if BBBanking pays its workers differently than other banks. State the null hypothesis: H 0 : _______________ State the alternative hypothesis: H a : _______________ Is this a one-tailed or two-tailed test? 1 2 Find the confidence interval: ______________ < µ < ______________ Make a decision (circle one): Reject H o Do Not Reject H o How did you make your decision? Briefly explain. Conclusion:

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STAT 008 | Lab #13 Page 4 of 6 STAT 008 AFlores 11.21 Critical Value Approach Refer to the BBBanking problem. Complete the hypothesis test of interest using the critical value approach. Test at the 5% level of significance. a) Perform a test to determine if BBBanking is underpaying its workers. State the null & alt. hypotheses: H 0 : ______________ vs. H a : ______________ Is this a one-tailed or two-tailed test? 1 2 Calculate the test statistic: t.s. = z = Find the critical value: c.v. = z = ______________ Make a decision (circle one): Reject H o Do Not Reject H o How did you make your decision? Include a sketch with your explanation. Conclusion: b) Perform a test to determine if BBBanking pays its workers differently than other banks. State the null & alt. hypotheses: H 0 : _____________ vs. H a : _____________ Is this a one-tailed or two-tailed test? 1 2 Calculate the test statistic and critical value: t.s. = z = __________ c.v. = z = _________ Make a decision (circle one): Reject H o Do Not Reject H o How did you make your decision? Include a sketch with your explanation. Conclusion:

STAT 008 | Lab #13 Page 5 of 6 STAT 008 AFlores 11.21 P-Value Approach Refer to the BBBanking problem. Complete the hypothesis test of interest using the p -value approach. Test at the 5% level of significance. Using Excel for Hypothesis Testing  Input the data in column A of Excel.  Click on an empty cell. Click Formulas  f x Insert Function  choose Statistical from the Category drop-down menu. Then under Select a Function choose Z.TEST. A dialog box will appear:  This function will report the p-value for a one-sided, greater-than alternative hypothesis. To obtain this p-value, type A1:A14 in the Array box. Then in the X box, type the value from the null hypothesis. In the Sigma box, type the known standard deviation. The p-value will appear in the window: Note: If your alternative hypothesis is a less-than alternative, subtract the reported p-value from 1 to obtain the appropriate p-value. For a two-sided alternative, if the reported p-value is less than 0.5, you should double it; otherwise, you should double (1-reported p-value). a) Perform a test to determine if BBBanking is underpaying its workers. State the null hypothesis: H 0 : ______________ State the alternative hypothesis: H a : ______________ Is this a one-tailed or two-tailed test? 1 2 Find the p- value & compare it to α: p-value: ____________ α = ______________ p-value

STAT 008 | Lab #13 Page 6 of 6 STAT 008 AFlores 11.21 Make a decision (circle one): Reject H o Do Not Reject H o Conclusion: b) Perform a test to determine if BBBanking pays its workers differently than other banks. State the null hypothesis: H 0 : ______________ State the alternative hypothesis: H a : ______________ Is this a one-tailed or two-tailed test? 1 2 Find the p-value & compare it to α: p-value: ______________ α = ____________ Make a decision (circle one): Reject H o Do Not Reject H o Conclusion: c) Perform a test to determine if BBBanking overpaying its workers. State the null hypothesis: H 0 : ______________ State the alternative hypothesis: H a : ______________ Is this a one-tailed or two-tailed test? 1 2 Find the p- value & compare it to α: p-value: ______________ α = ____________ Make a decision (circle one): Reject H o Do Not Reject H o Conclusion: You have completed your Lab. Please navigate to Canvas to submit your answers.

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