### Hypothesis Testing ExamplesBelow are examples of null and alternative hypotheses used in statistical hypothesis testing:1. **First Example:** - Null Hypothesis (\(H_0\)): \( p = 0.13 \) - Alternative Hypothesis (\(H_A\)): \( p > 0.13 \)2. **Second Example:** - Null Hypothesis (\(H_0\)): \( p = 0.20 \) - Alternative Hypothesis (\(H_A\)): \( p = 0.13 \)3. **Third Example:** - Null Hypothesis (\(H_0\)): \( p = 0.20 \) - Alternative Hypothesis (\(H_A\)): \( p \neq 0.20 \)4. **Fourth Example:** - Null Hypothesis (\(H_0\)): \( p = 0.20 \) - Alternative Hypothesis (\(H_A\)): \( p < 0.20 \)These examples illustrate different types of hypothesis tests:- **One-tailed test** (e.g., \( p > 0.13 \), \( p < 0.20 \))- **Two-tailed test** (e.g., \( p \neq 0.20 \)) A statistics instructor believes fewer than 20% of Clayton State University students attended the opening night midnight showing of the latest Marvel movie. She surveys 84 of her students and finds that 11 attended the midnight showing. Identify the correct null and alternative hypotheses:

The random variable is attending the midnight showing.We have to write the null and alternative…

Answered: A statistics instructor believes fewer…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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When two births are randomly selected, the sample space for genders is bb, bg, gb, and gg. Assume that those four outcomes are equally likely. Construct a table that describes the sampling distribution of the sample proportion of girls sample proportions equal the proportion of girls in two births? Does the result suggest that a sample proportion is an unbiased estimator of a population proportion? For the entire population, assume the probability of having a boy is is not affected by how many boys or girls have previously been born. Determine the probabilities of each sample proportion. Sample proportion of girls ▼ Does the mean of the sample proportions equal the proportion of girls in two births? O A. Yes, both the mean of the sample proportions and the population proportion are 4 1 O B. Yes, both the mean of the sample proportions and the population proportion are 3 O C. Yes, both the mean of the sample proportions and the population proportion are 1 2 O D. No, the mean of the…
The following is a random sample of men and women residents of Iowa. Do these data suggest a difference between the sexes in average spending on Christmas gifts in 2020? Follow the four steps for a hypothesis test. Male Male Female Female 250 450 300 375 400 300 350 400 425 350 500 450 350 325 425 300 500 425 400 350 400 200 350 370 375 450 400
A classic story involves four carpooling students who missed a test and gave as an excuse a flat tire. On the makeup test, the instructor asked the students to identify the particular tire that went flat. If they really didn't have a flat tire, would they be able to identify the same tire? A statistician asked 47 other randomly selected students to identify the tire they would select. The results are listed in the accompanying table. Use a 0.05 significance level to test the statistician's claim that the results fit a uniform distribution. What does the result suggest about the likelihood of four students identifying the same tire when they really didn't have a flat? Tire Number Selected Left Front 12 Right Front 8 ... Determine the null and alternative hypotheses. Ho: The tires are selected with the same frequency. H₁: At least one tire has a different frequency than the other tires. Calculate the test statistic, X². x² = (Round to three decimal places as needed.) Left Rear 14 Right…
2. A psychology class consists of 14 males and 36 females. If the professor selects names from the class list using random sampling, a. What is the probability that the first student selected will be a female? 8. I b. If a random sample of n = 3 stu dents is selected and the first two are both females, what is the prob- ability that the third student selected will be a male? CRE NA
A researcher is interested in whether self-proclaimed “cat people” are more introverted than self-proclaimed “dog people.” Select one: a. factorial ANOVA b. one sample t test c. paired samples t-test d. one-way ANOVA e. t-test independent means
1. An educational researcher says that the proportion of college students who study for their statistics final exam is 68%. Write the claim, null and alternative hypotheses for this statement. Draw a distribution to represent it, and then identify the type of test (tail) that should be used.
When two births are randomly selected, the sample space for genders is bb, bg. gb, and gg. Assume that those four outcomes are equally likely. Construct a table that describes the sampling distribution of the sample proportion of girls from two births. Does the mean of the sample proportions equal the proportion of girls in two births? Does the result suggest that a sample proportion an unbiased estimator of a population proportion? For the entire population, assume the probability of having a boy is the probability of having a girl is , and this is not affected by how many boys or girls have previously been born. 2 Determine the probabilities of each sample proportion. Probability Sample proportion of girls Tune intanare or cimnlifiad frartinne
A warehouse manager wants to know if there is an association between the shift worked and being on time for work. To investigate, he selects a random sample of 70 workers and classifies each one according to the shift they worked most recently and whether they were on time for work. He was unable to classify a substantial number of people as being on time, so he classified those individuals as unknown. The data are displayed in the table. The manager would like to know if these data provide convincing evidence of an association between the shift worked and being on time in the large population of all workers at this warehouse. The random and 10% conditions are met. Is the Large Counts condition met? Yes, the smallest expected count is 5, so all expected counts are at least 5. Yes, the smallest expected count is 8.54, so all expected counts are at least 5. No, the smallest expected count is 2.56, so the expected counts are not all at least 5. No, the smallest expected count is…
2. Toastmasters International cites a report by Gallup Poll that 40% of Americans fear public speaking. A student believes that less than 40% of students at her school fear public speaking. She randomly surveys 361 schoolmates and finds that 137 report they fear public speaking. Conduct a hypothesis test at the 5% level to determine if the percent at her school is less than 40%. a. State the null hypothesis. b. State the alternative hypothesis. c. Construct a 95% confidence interval for the true proportion. Sketch the graph of the situation. Label the point estimate and the lower and upper bounds of the confidence interval. (Round your answers to four decimal places.)
2. A political scientist developed a test designed to measure the degree of awareness of current events. She wants to estimate the average score that would be achieved on this test by all students in a certain high school. The administration at the school will not allow the experimenter to randomly select students out of classes in session, but it will allow her to interrupt a small number of classes for the purpose of giving the test to every member of the class. Thus, the experimenter selects 25 classes at random from the 108 classes in session at a particular hour. The test is given to each member of the sampled classes, with results as shown in the accompanying table. Number of students, mi Total score, yi Class 1 31 1590 2 29 1510 3 25 1490 4 35 1610 5 15 800 6 31 1720

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