Chapter 9 Hypothesis Testing Lab - Hope Hendren

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Apr 3, 2024

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NAME Hope Hendren CHAPTER 7 Hypothesis Testing Lab (adapted from OpenStax 9.1) Directions: Make a new copy of this document. Type your name on the document, and type your answers ( in red would be great ) to the BOLD questions that need to be answered. I have collected the data and have begun each hypothesis test for you. Just complete the test, state the conclusion and answer all the questions in BOLD . Let’s all use the level of significance as α = .05 (The original lab is given as a link in Moodle from Open Stax textbook) Television Survey In a recent survey, it was stated that Americans watch television on average four hours per day. Assume that σ = 2. Using the sample obtained, conduct a hypothesis test to determine if the average for students at your school is lower. 1. H 0 : μ = 4 hours 2. H a : μ < 4 hours 3. In words, define the random variable. x = mean hours, TV watching per day by SCHS students 4. The distribution to use for the test is Z. 5. Determine the test statistic using your data. Use x = 2.18 hours (average from my survey sent to my students at SCHS n = 49 responses, reminder, we have a known value σ = 2 ) The test statistic: Z = 2.18 − 4 2 / √ ❑ = -6.37 ( check on calculator) - Z-Test 6. DETERMINE THE P-value ( show your work, what did you type on your calculator) Z-Test (Input: Stats, μ 0:4 ,σ :2 , x :2.18 ,n :49 , μ : < μ 0 ¿ = 9.494 E -11 ≈ 0 7. Do you or do you not reject the null hypothesis? Why? I reject the null hypothesis because 0 (P-value) is less than .05 (Alpha). There is significant statistical evidence to prove that the students at SCHS watch less TV than the national average (4 hours). 8. Write a clear conclusion using a complete sentence. There is significant evidence according to the statistical data to show that SCHS students watch less TV than the national average. The P-value of the SCHS student's data is less than the significance level of the national average, therefore we reject the null hypothesis. Language Survey

https://www.ncdemography.org/2014/02/17/top-10-non-english-languages-spoken-in-north- carolina/ About 42.3% of Californians, about 11% of North Carolinians, and about 19.6% of all Americans over age five speak a language other than English at home. (About 11% of North Carolinians- using google ) Using the sample that I obtained, conduct a hypothesis test to determine if the percent of the students at your school who speak a language other than English at home is different from 11.0% ( I changed this from the lab: compare SCHS to all North Carolinians, not Californians) 1. H 0 : p = .11 (11%) 2. H a : p ≠ .11 3. In words, define the random variable. ^ p = the percentage of students at SCHS that speak a language other than English at home. 4. The distribution to use for the test is 1-PropZTest. 5. Determine the test statistic using your data. Use x = 5 , so ^ p = ( 10.6% from my survey sent to my students n = 47 ) The test statistic Z = 5 49 − .11 √ ❑ = .079 ( check on calculator) 6. DETERMINE THE P-value P = .9368 ( use the calculator, no work needs to be shown) 7. Do you or do you not reject the null hypothesis? Why? I do not reject the null hypothesis because the P-value is greater than the significance level (.9368 > .05). 8. Write a clear conclusion using a complete sentence. The P-value is greater than the significance level, therefore there is not enough evidence to reject the null hypothesis. This means that the percent of students at my school that speak a language other than english at home cant not be denied to be 11%. Jeans Survey Suppose that young adults own an average of three pairs of jeans. Survey eight people from your class to determine if the average is higher than three. Assume the population is normal. 1. H 0 : μ = 3 jeans

2. H a : μ > 3 3. In words, define the random variable. x = average number of jeans owned by 8 young adults that were asked 4. The distribution to use for the test is T. 5. Determine the test statistic using your data. Use this data we collected: 15 4 5 8 10 2 11 10 ( 8 students were asked how many pairs of jeans they own and above are the responses) The test statistic = T = 3.4 ( use the calculator, no work needs to be shown ) 6. DETERMINE THE P-value ( use the calculator, no work needs to be shown ) P = .0057 7. Do you or do you not reject the null hypothesis? Why? I reject the null hypothesis because the P-value is less than alpha (.0057 < .05). 8. Write a clear conclusion using a complete sentence. There is statistically significant evidence to reject the null hypothesis because the P-value is less than alpha. This means that on average 8 people in my class own more pairs jeans than an average of 3 pairs of jeans. Continue on Next page - two questions Two General Questions to answer below: ( Fill in the blanks and answer the questions in bold) 1. I collected the data by sending out a survey to the students: SCHS Survey. I wanted to have at least 30 students for the television survey, without more than 30 , I would need to show the distribution is normal. These are the assumptions needed for a Test about z.

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This is true for a Test about t as well, but in the Jeans survey n= 8, therefore, what was stated instead was normally distributed . For the language survey, a Test about p, np > 5 is an assumption for testing. We did not meet this assumption because x = 5 , but we completed the test anyways. For all three Tests that we have been studying, the data we collect for testing must be an SRS. What does this stand for and was the data I collected an SRS? SRS - Simple Random Sampling. SRS is important to use when collecting data because it reduces bias and allows all units in the population have an equal chance of being selected. Yet in these three studies, we used convenience sampling because it was taken from a specific population (students in a stats class). Describe the bias in my sample given the conditions in which I collected the data. The bias in these samples is due to the fact that it was taken from highschool students in a stats class. Most students are ages 17-18 and live in a similar area with similar ideologies. 2. This lab was a collection of all three Tests that we have studied in Chapter 7. It also represented one of each: right, left, and two-tailed For each survey below write next to it which type of tailed test it was. TELEVISION Survey - Left-tailed test Language Survey - Two-tailed test Jeans Survey - Right-tailed test