Instruction for Week 10 Homework There are two deliverables for this week's homework. 1. An Excel file with the calculation of Hypothesis Testing for proportions. 2. A Microsoft Word file contains the write-up of the analysis and answers to the questions. The Hypothesis Testing for proportions Calculation To help you do the calculation, you have been provided with an Excel file \"Hypothesis Testing & Confidence Level template v6\". Use this template to complete the analysis. This template contains various Hypothesis Testing calculations. You will be using the sheet \"HT Proportion\" for your homework. It is the \"brown\" colored tab sheet. In order to preserve the embedded formulas, you are only allowed to input numbers into the \"green\" cells. I encourage you to explore how the embedded formulas were implemented. We will have a Live Help session to explain how to use the template. Please go to Instructor Insights to register. This Excel file accounts for 20 points of your homework grade. The Write-up The write-up should include the Hypothesis Testing analysis and answers to the questions. The write-up must be in Microsoft Word. You are provided with a reference answer. The write-up accounts for 10 points of your homework grade. A pizza shop claims that its mean delivery time is less than 30 minutes. A random selection of 36 delivery times has a sample mean of 28.5 minutes and a standard deviation of 3.5 minutes. Is there enough evidence to support the claim at the significance level alpha = 0.05? Claim Null Hypothesis H0 Alternate Hypothesis Ha: Test Type Sample Size n Population Mean Sample Mean xbar Standard Deviation Confidence Level Significance Level Test Statistics P-value P-Value Test Decision Conclusion n xbar 1- z p < >= < : = = = = = = = = 30 30 30 Left-tailed 36 30 28.5 3.5 0.95 0.05 -2.57142857 0.005063995 Test Statistics z Test Type Left-tailed Right-tailed Two-tailed alpha Left Tail Critical Valu Right Tail Critical Va Two Tail Critical Val Reject H0 At 0.05 level of significance, we have sufficient evidence to conclude < 30 delivery times dence to support -2.5714285714 P-value 0.0050639953 0.9949360047 0.0101279905 0.05 -1.644853627 1.644853627 -1.9599639845 1.9599639845 A dealer claims the mean price of a 2005 Honda Pilot is at least $23900. You suspect the claim is incorrect and find a sample of 14 similar vehicles has a mean price of $23000 and a standard deviation of $1113. Is there enough evidence to rejcet the dealer's claim at alpha=0.05 Claim Null Hypothesis H0 Alternate Hypothesis Ha: Test Type Sample Size n Population Mean Sample Mean xbar Standard Deviation s Confidence Level Significance Level Test Stat t d.f. (degree of freedom) P-value n xbar s 1- t d.f. p-value >= >= < : = = = = = = = = = 23900 23900 23900 Left-tailed 14 23900 23000 1113 0.95 0.05 -3.025599 13 0.00487349 P-Value Test Compare P with alpha Decision P <= > : = = = = = = = 0.5 0.5 0.5 Right-tailed 15 0.5 0.666666667 (phat=x/n) 1.290994449 0.95 0.05 0.098352801 P-value > Fail to reject H0 At 0.05 level of significance, we do not have sufficient evidence to support the claim p > 0 Test Stat z Test Type Left-tailed Right-tailed Two-tailed 1.2909944487 P-value alpha Left Critical Value -zc Right Critical Value zc Two Tail Critical Values ient evidence to support the claim p > 0.5 0.9016471988 0.0983528012 0.1967056025 0.95 1.644853627 1.644853627 -0.0627067779 0.0627067779 The average absorbency of 10 rolls of Brand X paper towel is 488.5 with standard deviation 10.5. The average absorbency of 10 rolls of Brand Z paper towel is 492.9 with standard deviation 16.4. Is this enough evidence to support the claim that with 0.5 significance level the two branad's absorbencies are different? Claim Null Hypothesis H0 Alternate Hypothesis Ha: Test Type Population Average Difference Sample #1 Size Sample #1 average Sample #1 Standard Deviation Sample #2 Size Sample #2 average Sample #2 Standard Deviation Sample Average Difference Pooled Sandard Deviation Confidence Level Significance Level Test Statistics Degree of Freedom P-value 1-2 1-2 1-2 <> = <> : = = = = = = = = = = = = = = 0 0 0 1-2 n1 xbar1 s1 n2 xbar2 s2 xbar1 - xbar2 sp 1- t d.f. p P-Value Test Decision Conclusion Failed to Reject H0 At 0.05 level of significance, we do not have sufficient evidence to conclude 1-2 <> 0 Two-tailed 0 10 488.5 10.5 10 492.9 16.4 -4.4 13.76971314 0.95 0.05 -0.71451736 18 0.484071529 Test Stat t Test Type Left-tailed Right-tailed Two-tailed alpha Left Tail Critical RightTail Critical Two Tail Critical -0.7145173614 P-value 0.2420357647 0.2420357647 0.4840715294 0.05 -1.7340635923 1.7340635923 -2.1009220369 2.1009220369 evidence to conclude 1-2 <> 0 In a survey of 200 female and 250 male internet users, 30% of the females an 38% males said they plan to shop online. At 90% confidence level, is there a difference between the proportions of female and male internet users who plan to shop online? Claim Null Hypothesis H0 Alternate Hypothesis Ha: Test Type Sample #1 Size Sample #1 Proportion Sample #2 Size Sample #2 Proportion Pooled Proportion Confidence Level Significance Level Test Statistics P-value P-Value Test Decision Conclusion 1-2 1-2 1-2 n1 p1 n2 p2 P 1- z p <> = <> : = = = = = = = = 0 0 0 Two-tailed 200 0.3 250 0.38 0.344444444 0.9 0.1 -1.77461598 0.075961316 Test Statistics z Test Type Left-tailed Right-tailed Two-tailed alpha Left Tail Critical Valu Right Tail Critical Va Two Tail Critical Val Reject H0 At 0.01 level of significance, we have sufficient evidence to conclude 1-2 <> 0 es said they plan to shop online. male internet users -1.7746159843 P-value 0.0379806581 0.9620193419 0.0759613161 0.1 -1.2815515655 1.2815515655 -1.644853627 1.644853627 ce to conclude 1-2 <> 0 MAT 510 - Homework Assignment Homework Assignment 9 Due in week 10 and worth 30 points Suppose that there are two (2) candidates (i.e., Jones and Johns) in the upcoming presidential election. Sara notes that she has discussed the presidential election candidates with 15 friends, and 10 said that they are voting for candidate Jones. Sara is therefore convinced that candidate Jones will win the election because Jones gets more than 50% of votes. Answer the following questions in the space provided below: 1. Based on what you now know about statistical inference, is Sara's conclusion a logical conclusion? Why or why not? Statistical inference is the process of drawing conclusions about populations or scientific truths from data. Sara did not collect large enough of populations to draw a logical conclusion that Jones will win. More the 15 people will be allowed to vote on the presidential election. 2. How many friend samples Sara should have in order to draw the conclusion with 95% confidence interval? Why? The population size is unknown. Knowing the population of those that will vote in the presidential election will help determine the sample size need to draw a conclusion of 95% confidence interval. Once the sample constitute a small share of the population, the size of the population matters. As the population increases the sample size needed for a given confidence interval increases (proportionally), until it becomes relatively constant, for example: Population 10 50 100 200 500 1000 3000 100000+ Sample 10 44 80 132 217 278 341 385 3. How would you explain your conclusion to Sara without using any statistical jargon? Why? The 15 friends Sara asked about their vote is not a good representation of everyone who will vote overall. Presidential elections typically involve thousands of voters not just 15. A person can't say they hate all fruits based on taking a single bite out of a grape, which is only one type of fruit. Sara has a 50/50 chance in being right, which is always the case when there are only two things to choose from and the option to choose nothing isn't an option. Type your answers below and submit this file in Week 10 of the online course shell