Week 5 1

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Southern Illinois University, Edwardsville *

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Statistics

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Apr 3, 2024

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Problem 15.2 a. Null and alternative Hypothesis: Ho: π ≥ 0.30 H1: π < 0.30 b. Type I and type II errors that could occur in hypothesis testing: Rejecting the null hypothesis when it is true. In this context, it would mean deciding to change the advertising campaign when 30% or more of the consumers like it. Failing to reject the null hypothesis when it is false. In this context, it would mean not changing the advertising campaign when less than 30% of the consumers like it. c. Since we are examining a single percentage and trying to determine if it is less than a certain number (30%), the statistical test to employ would be a one-sided hypothesis test for proportions, more precisely a z-test for proportions. d. Given a random sample of 300 consumers, where 84 respondents indicated that they liked the campaign, we can conduct a hypothesis test. Using a z-test for proportions: Given, Sample size (n)= 300 No of respondents who liked the campaign (x)= 84 Null hypothesis = Ho: π ≥ 0.30 Alternative hypothesis = H1: π < 0.30 Value of the sample proportion (p) = 84/300 = 0.28 z = p-π σ p where, σ p = ¿ 0.02683 Now, z= 0.28-0.30 0.02683 = -0.745 As the calculated p value (0.28) is greater than 0.05, then we would fail to reject the null hypothesis.

Problem 15.3 (attached with this word file) a. Is there evidence that an average of more than 50 refrigerators per store were sold during this sale? Use a = 0.05. Answer: No, there is not enough evidence to support the claim that an average of more than 50 refrigerators per store were sold. The p-value of 0.111 is greater than the significance level of 0.05. Therefore, we fail to reject the null hypothesis. b. What assumption is necessary to perform this test? Answer: The assumption necessary to perform this one-sample t-test is that the sample is a random sample from a normally distributed population.

Chapter 14, Problem 2 (9,10 &11) Column Number Variable number Variable Name Question Number Coding Instructions 1 1 Batteries 9 Assign a numerical code on the circled category: 1=Not so Important 5=Very Important 2 2 Automatic Mode 9 Assign a numerical code on the circled category: 1=Not so Important 5=Very Important 3 3 Aperture Control 9 Assign a numerical code on the circled category: 1=Not so Important 5=Very Important 4 4 LCD Screen 9 Assign a numerical code on the circled category: 1=Not so Important 5=Very Important 5 5 Outlet- Drugstore 10 Code option as binary variable. 0= Not selected 1= Selected 6 6 Outlet- Camera store 10 Code option as binary variable. 0= Not selected 1= Selected 7 7 Outlet- Discount/ Mass- Merchandiser 10 Code option as binary variable. 0= Not selected 1= Selected 8 8 Outlet- Electronics store 10 Code option as binary variable. 0= Not selected 1= Selected 9 9 Outlet- Internet 10 Code option as binary variable. 0= Not selected 1= Selected 10 10 Outlet- Other 10 Code option as binary variable. 0= Not selected 1= Selected

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