5.A teacher believes that the average exam scores of her current class is higher than thehistorical average of 75. She takes a random sample from her class with scores:77, 80, 74, 76, 82, 77, 79, 76, 81Formulate and implement a one-sided hypothesis test to evaluate the teacher's claim at the 5% level.You may use that the standard deviation of the sample is approximately 2.5.

We have given the average exam scores of a class.77, 80, 74, 76, 82, 77, 79, 76, 81Population mean μ…

Answered: 5. A teacher believes that the average…

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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6. A psychology professor of a large class became curious as to whether the students who turned in tests first scored differently from the overall mean on the test. The overall mean score on the test was 75 with a standard deviation of 10; the scores were approximately normally distributed. The mean score for the first 20 students to turn in tests was 78. Using the .05 significance level, was the average test score earned by the first 20 students to turn in their tests significantly different from the overall mean?
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Suppose a test is given to 20 randomly selected college freshmen in Ohio. The sample average score on the test is 12 points and the sample standard deviation is 4 points. Suppose the same test is given to 16 randomly selected college freshmen in Iowa. The sample average score on the test is 8 points and the sample standard deviation is 3 points. We want to test whether there is a significant difference in scores of college freshmen in Ohio versus Iowa. What is the point estimate for the difference in population means, where difference is defined as (Ohio minus Iowa)?
As Director of Admissions at Garden Valley University, you believe that the average age of full-time students (Group 1) is less than the average age of part-time students (Group 2). You sample 45 full-time students, and the sample mean age is 22.3 with a standard deviation of 4.8. You sample 50 part-time students, and the sample mean age is 24.3 with a standard deviation of 5.6. Test the claim using a 2% level of significance. Assume the population standard deviations are unequal and that both populations are normally distributed. Where necessary, round results accurate to 4 decimal places. a. What are the correct hypotheses? Null: Ο Ho: μ = 0 O Ho: ₁ = ₂ Ho: M₁ M₂ Ο Ho: μ = 22.3 Alternative: Ο HA: Mı # με Ο HA: μ. > με HA: ₁2 HA: < 0 Ο HA: μ + 22.3 b. What is the correct distribution to use for the test? Select an answer c. What is the test statistic? d. What is the p-value? p-value = e. The correct decision is to Select an answer f. INTERPRET the conclusion in the context of the…
Fran is training for her first marathon, and she wants to know if there is a significant difference between the mean number of miles run each week by group runners and individual runners who are training for marathons. She interviews 42 randomly selected people who train in groups and finds that they run a mean of 47.1 miles per week. Assume that the population standard deviation for group runners is known to be 4.4 miles per week. She also interviews a random sample of 47 people who train on their own and finds that they run a mean of 48.5 miles per week. Assume that the population standard deviation for people who run by themselves is 1.8 miles per week. Test the claim at the 0.01 level of significance. Let group runners training for marathons be Population 1 and let individual runners training for marathons be Population 2. Step 2 of 3 : Compute the value of the test statistic. Round your answer to two decimal places.
The honors program at Brad's university only accepts students with an entrance exam score over 400. What percentage of students would be eligible if the students at Brad's school have an average exam score of 250, with a standard deviation of 80?
Suppose an education administrator wants to know whether the test scores of a new standardized graduation exam are different for males and females. To test this hypothesis, the administrator decides to perform a ?‑test for two independent means. She takes a random sample of test scores from both male and female populations. Some of the summary data are shown in the table. Population PopulationDescription Samplesize Samplemean (pts) Sample standard deviation (pts) 1 Female ?1=21 ?⎯⎯⎯1=34.3 ?1=3.09 2 Male ?2=22 ?⎯⎯⎯2=34.7 ?2=3.82 The administrator assumes that the population variances are equal, so she computes a pooled ?‑test statistic. Determine the number of degrees of freedom, df, for the pooled ?‑statistic.
Good credit: The Fair Isaac Corporation (FICO) credit score is used by banks and other lenders to determine whether someone is a good credit risk. Scores range from 300 to 850, with a score of 720 or more indicating that a person is a very good credit risk. An economist wants to determine whether the mean FICO score is more than the cutoff of 720. She finds that a random sample of 40 people had a mean FICO score of 760 with a standard deviation of 95. Can the economist conclude that the mean FICO score is greater than 720? Use the a = 0.05 level of significance and the P-value State the appropriate null and alternate hypotheses. Compute the value of the test statistic. Round the answer to at least three decimal places. Input the correct interval for the P-value. Determine whether to reject H0 State a conclusion.
A bottled water distributor wants to determine whether the mean amount of water contained in 1-gallon bottles purchased from a nationally known water bottling company is actually 1 gallon. You know from the water bottling company specifications that the standard deviation of the amount of water is 0.02 gallon. You select a random sample of 50 bottles, and the mean amount of water per 1-gallon bottle is 0.992 gallon. What is the test statistic?
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Good credit: The Fair Isaac Corporation (FICO) credit score is used by banks and other lenders to determine whether someone is a good credit risk. Scores range from 300 to 850, with a score of 720 or more indicating that a person is a very good credit risk. An economist wants to determine whether the mean FICO score is more than the cutoff of 720. She finds that a random sample of 40 people had a mean FICO score of 760 with a standard deviation of 95. Can the economist conclude that the mean FICO score is greater than 720? Use the α= 0.01 level of significance and the P-value method and Excel. a)Compute the value of the test statistic. Round the answer to at least three decimal places. t= ? b) what is the P-value? c) Does it Rejects/Accepts the null hypothesis H_0? d) There is/ is not enough evidence to conclude that the mean FICO score is lower than the cutoff of 720.

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