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1. The average height of all previous contestants in a beauty pageant has been 180 cm with a standard deviation of 5 cm. Is there a reason to believe that there has been a change in the average height if a random sample of 50 new contestants has an average height of 178 cm? Use a 0.05 level of significance.

1. The average height of all previous contestants in a beauty pageant has been 180 cm with a standard deviation of 5 cm. Is there a reason to believe that there has been a change in the average height if a random sample of 50 new contestants has an average height of 178 cm? Use a 0.05 level of significance.

MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
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1. The average height of all previous contestants in a beauty pageant has been 180 cm with a standard deviation of 5 cm. Is there a reason to believe that there has been a change in the average height if a random sample of 50 new contestants has an average height of 178 cm? Use a 0.05 level of significance. 2. A fitness center claims that its members lose at least 5 kg after one month of joining the center. An independent agency would like to verify whether such claim is credible. The agency took a random sample of 25 newly recruited members and found that they lost an average of 4.75 kg within the first month with a standard deviation of 1.5 kg. What is the agency's conclusion at 0.05 level of significance?
Transcribed Image Text:1. The average height of all previous contestants in a beauty pageant has been 180 cm with a standard deviation of 5 cm. Is there a reason to believe that there has been a change in the average height if a random sample of 50 new contestants has an average height of 178 cm? Use a 0.05 level of significance. 2. A fitness center claims that its members lose at least 5 kg after one month of joining the center. An independent agency would like to verify whether such claim is credible. The agency took a random sample of 25 newly recruited members and found that they lost an average of 4.75 kg within the first month with a standard deviation of 1.5 kg. What is the agency's conclusion at 0.05 level of significance?
A. Write down the null and alternative hypotheses. Express them symbolically. Example: Ho: u<0.5 H1: u > 0.5 B. Identify the type of tes. Example: t-test, two populations, right-tailed C. Identify the rejection region. You should indicate the critical value and degrees of freedom, df, (if applicable) Examples: z> 1.96 (critical value = 0.025) t> 2.571 (critical value = 0.025, df = 5) %3D D. Solve for the test statistic E. Give the appropriate conclusion, Your conclusion must be based on the claim mentioned in the problem. Just saying that the null hypothesis is rejected or accepted is not enough., Example: There is sufficient evidence to show that the mean P3 score of 4BSCE-01 students is greater than 94. Express your answers in 3 decimal places. Box your answers.
Transcribed Image Text:A. Write down the null and alternative hypotheses. Express them symbolically. Example: Ho: u<0.5 H1: u > 0.5 B. Identify the type of tes. Example: t-test, two populations, right-tailed C. Identify the rejection region. You should indicate the critical value and degrees of freedom, df, (if applicable) Examples: z> 1.96 (critical value = 0.025) t> 2.571 (critical value = 0.025, df = 5) %3D D. Solve for the test statistic E. Give the appropriate conclusion, Your conclusion must be based on the claim mentioned in the problem. Just saying that the null hypothesis is rejected or accepted is not enough., Example: There is sufficient evidence to show that the mean P3 score of 4BSCE-01 students is greater than 94. Express your answers in 3 decimal places. Box your answers.
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