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Problem 1: Figure 1 shows the histogram of the current salary (in thous. USD) of a sample which includes 474 workers. Frequency 120- 100- Figure 1 80- 60- 40- 20- 6 10000 20000 Histogram 30000 40000 CURRENT SALARY 50000 60000 Mean 13767.83 Std. Dev.-6830.265 N-474 a. Can we standardise from this distribution, then apply the law of three sigmas? Explain why? b. Assume that the distribution in Figure 1 is FOR A POPULATION, which follows the normal distribution. What is the probability of of a randomly selected person who has current salary greater than $15000? c. Come back to the real situation where the distribution in Figure 1 is for a sample but assume that the sample size is large enough for the Central Limit Theorem to hold. Test the null hypothesis that the average current salary is $15000 at the 5% level of significance. Which method of decision rules do you use? d. Construct the 95% CI for the current salary and based on this confidence interval, test the hypothesis that the current salary is $14000.

Problem 1: Figure 1 shows the histogram of the current salary (in thous. USD) of a sample which includes 474 workers. Frequency 120- 100- Figure 1 80- 60- 40- 20- 6 10000 20000 Histogram 30000 40000 CURRENT SALARY 50000 60000 Mean 13767.83 Std. Dev.-6830.265 N-474 a. Can we standardise from this distribution, then apply the law of three sigmas? Explain why? b. Assume that the distribution in Figure 1 is FOR A POPULATION, which follows the normal distribution. What is the probability of of a randomly selected person who has current salary greater than $15000? c. Come back to the real situation where the distribution in Figure 1 is for a sample but assume that the sample size is large enough for the Central Limit Theorem to hold. Test the null hypothesis that the average current salary is $15000 at the 5% level of significance. Which method of decision rules do you use? d. Construct the 95% CI for the current salary and based on this confidence interval, test the hypothesis that the current salary is $14000.

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
Problem 1P
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Problem 1: Figure 1 shows the histogram of the current salary (in thous. USD) of a sample which includes 474 workers. a. Frequency 120- Figure 1 100- 80- 60- 40- 20- 0 10000 20000 Histogram 30000 40000 CURRENT SALARY 50000 60000 Mean 13767.83 Std. Dev.-6830.265 N-474 Can we standardise from this distribution, then apply the law of three sigmas? Explain why? b. Assume that the distribution in Figure 1 is FOR A POPULATION, which follows the normal distribution. What is the probability of of a randomly selected person who has current salary greater than $15000? c. Come back to the real situation where the distribution in Figure 1 is for a sample but assume that the sample size is large enough for the Central Limit Theorem to hold. Test the null hypothesis that the average current salary is $15000 at the 5% level of significance. Which method of decision rules do you use? d. Construct the 95% CI for the current salary and based on this confidence interval, test the hypothesis that the current salary is $14000.
Transcribed Image Text:Problem 1: Figure 1 shows the histogram of the current salary (in thous. USD) of a sample which includes 474 workers. a. Frequency 120- Figure 1 100- 80- 60- 40- 20- 0 10000 20000 Histogram 30000 40000 CURRENT SALARY 50000 60000 Mean 13767.83 Std. Dev.-6830.265 N-474 Can we standardise from this distribution, then apply the law of three sigmas? Explain why? b. Assume that the distribution in Figure 1 is FOR A POPULATION, which follows the normal distribution. What is the probability of of a randomly selected person who has current salary greater than $15000? c. Come back to the real situation where the distribution in Figure 1 is for a sample but assume that the sample size is large enough for the Central Limit Theorem to hold. Test the null hypothesis that the average current salary is $15000 at the 5% level of significance. Which method of decision rules do you use? d. Construct the 95% CI for the current salary and based on this confidence interval, test the hypothesis that the current salary is $14000.
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