10-we know the population mean for turnover intentions is μ = 2.00. Is the mean for our current sample of employees significantly different from the population mean? Use an α = .01. Compute t-obs. A researcher was interested in studying the effects of job insecurity on employee job attitudes. Half of the research participants were randomlyassigned to experience high insecurity (manipulated by announcing 50% layoffs) and half were assigned to experience low insecurity (announcementof 5% layoffs). In addition, the researcher was also interested in whether or not the method by which the layoffs were to occur would influence jobattitudes and perceived fairness. Therefore, half of the research participants were assigned to a fair layoff condition (i.e., layoffs determined by jobperformance) and half were assigned to an unfair condition (i.e., layoffs determined by favoritism). Employees were asked to make ratings on severalissues: how important their jobs were ("job importance"), the extent to which they intended to quit working for the organization ("turnoverintentions"), their perceived chances of being laid off ("chances of being laid off"), and perceptions of fairness ("perceived fairness"). Finally, they wereasked to decide whether they wanted to quit working for the organization or remain employed with the organization ("decision to quit").'5 or 50% Layoff Fair/UnfairJobTurnoverChances of Perceived DecisionConditionMethod Importance Intentions Being Laid Off Fairnessto Quit43712375211210124511352114357123475221211021347521121032757116.24502222501216325322225012122502224350212235012225522435021Coding Manual: Layoff Condition: 1= 5% 2 = 50%Fairness Condition: 1 = Fair 2 = UnfairDecision to Quit: 1= Quit 2= Remain

Find the mean of turnover interventions: The mean of turnover interventions is obtained as 2.65 from the calculation given below: Thus, the mean of turnover interventions is 2.65.Find the variance of turnover interventions: The standard deviation of turnover interventions is obtained as 0.9881 from the calculation given below: Thus, the standard deviation of turnover interventions is 0.9881.Null and alternate hypotheses: The investigator is specially interested to test whether the population mean for turnover interventions is equal to 2 or not. Denote the population mean for turnover interventions as μ. The hypotheses are given below: Null hypothesis: H0 : μ = 2 That is, the population mean for turnover interventions is equal to 2. Alternative hypothesis: Ha : μ ≠ 2 (Two tail test). That is, the population mean for turnover interventions is significantly different from 2. Type of test statistic: The objective is to test for the significance of population mean. Here, the population standard deviation is unknown and the population from which the sample is drawn follows approximately normal distribution. Thus, a single sample t test is appropriate for the given situation.Compute the test statistic value t-obs: The sample size is n = 20. The sample mean is x-bar = 2.65. The sample standard deviation is s = 0.9881. The test statistic value t-obs is obtained as 2.94 from the calculations given below: Thus, the test statistic value t-obs is 2.94 Critical value: The level of significance is α = 0.01. The critical value is obtained as ±2.8609 from the calculation given below: Since, the t-distribution is symmetric, the two critical values are –t(α/2) = -2.8609 and +t(α/2) = +2.8609.Decision rule: Denote t as test statistic value and t(α/2) as the critical value. Decision rule based on critical approach: If t ≤ –t(α/2) (or) t ≥ t(α/2), then reject the null hypothesis H0. If –t(α/2) < t < t(α/2), then fail to reject the null hypothesis H0. Conclusion: Conclusion based on critical value approach: The test statistic value is 2.94 and critical value is ±2.8609. Here, t ≥ t(α/2). That is, 2.94 (=t) > 2.8609 (= t(α/2)). By the rejection rule, reject the null hypothesis H0. Therefore, the population mean for turnover interventions is significantly different from 2. Hence, at the 0.01 level of significance, there is enough evidence to conclude that the mean for our current sample of employees significantly different from the population mean.

Answered: we know the population mean for…

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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10-

we know the population mean for turnover intentions is μ = 2.00. Is the mean for our current sample of employees significantly different from the population mean? Use an α = .01.

A researcher was interested in studying the effects of job insecurity on employee job attitudes. Half of the research participants were randomly
assigned to experience high insecurity (manipulated by announcing 50% layoffs) and half were assigned to experience low insecurity (announcement
of 5% layoffs). In addition, the researcher was also interested in whether or not the method by which the layoffs were to occur would influence job
attitudes and perceived fairness. Therefore, half of the research participants were assigned to a fair layoff condition (i.e., layoffs determined by job
performance) and half were assigned to an unfair condition (i.e., layoffs determined by favoritism). Employees were asked to make ratings on several
issues: how important their jobs were ("job importance"), the extent to which they intended to quit working for the organization ("turnover
intentions"), their perceived chances of being laid off ("chances of being laid off"), and perceptions of fairness ("perceived fairness"). Finally, they were
asked to decide whether they wanted to quit working for the organization or remain employed with the organization ("decision to quit").'
5 or 50% Layoff Fair/Unfair
Job
Turnover
Chances of Perceived Decision
Condition
Method Importance Intentions Being Laid Off Fairness
to Quit
4
3
7
1
2
3
75
2
1
1
2
10
1
2
4
5
1
1
3
5
2
1
1
4
3
5
7
1
2
3
4
75
2
2
1
2
1
10
2
1
3
4
75
2
1
1
2
10
3
2
75
7
1
1
6.
2
4
50
2
2
2
2
50
1
2
1
6
3
25
3
2
2
2
2
50
1
2
1
2
2
50
2
2
2
4
3
50
2
1
2
2
3
50
1
2
2
25
5
2
2
4
3
50
2
1
Coding Manual: Layoff Condition: 1= 5% 2 = 50%
Fairness Condition: 1 = Fair 2 = Unfair
Decision to Quit: 1= Quit 2= Remain

Definition Definition Measure of central tendency that is the average of a given data set. The mean value is evaluated as the quotient of the sum of all observations by the sample size. The mean, in contrast to a median, is affected by extreme values. Very large or very small values can distract the mean from the center of the data. Arithmetic mean: The most common type of mean is the arithmetic mean. It is evaluated using the formula: μ = 1 N ∑ i = 1 N x i Other types of means are the geometric mean, logarithmic mean, and harmonic mean. Geometric mean: The nth root of the product of n observations from a data set is defined as the geometric mean of the set: G = x 1 x 2 ... x n n Logarithmic mean: The difference of the natural logarithms of the two numbers, divided by the difference between the numbers is the logarithmic mean of the two numbers. The logarithmic mean is used particularly in heat transfer and mass transfer. ln x 2 − ln x 1 x 2 − x 1 Harmonic mean: The inverse of the arithmetic mean of the inverses of all the numbers in a data set is the harmonic mean of the data. 1 1 x 1 + 1 x 2 + ...

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