Need help with b and d. A and C are correct. (1 point) Hourly wages at Manufactu
ID: 3039978 • Letter: N
Question
Need help with b and d.
A and C are correct.
(1 point) Hourly wages at Manufacturing Plant A very from worker to worker, with an average hourly wage of $13.71, and a standard deviation of $2.5 per hour, or PlantA-2.5. In an attempt to attract new employees, a newly constructed Manufacturing Plant B claims that its employees will be paid, on average, more than than employees at Manufacturing Plant A. Assume that the standard deviation in hourly wages at Plant B is the same as at Plant A, or PlamB = 2.5 (a) Choose the correct statistical hypotheses. HA-AnantB = 13.71 HA-XplantB > 13.71 HA-AnantB13.71 HA-XplantB 13.71 A. Ho : PlanB > 13.71 B. Ho : X Plan:B = 13.71 C. Ho : Anant = 13.71 D. Ho : XPlantB > 13.71 OE. Ho : Plant,-13.71 F. Ho : PlantB A : PlantB (b) Statistical testing of the null hypothesis is to be carried out by randomly selecting 38 employee:s at Plant B. If the mean/average hourly wage of these 38 employees is greater than $14.62, then there is enough statistical evidence to indicate that the mean hourly wage of employees at Plant B is greater than the mean hourly wage of employees at Plant A. What level of was used here? Enter your answer to at least three decimal places 0.9876 (c) The average of the sample of n = 38 workers was found to be X-14.27. What decision can you make from this sample? A. The sample size is too small to conduct a statistical test, so a decision cannot be made B. Employees at Plant B do earn more on average compared to employees at Plant A - C. The hourly wages at Plant B need to be Normally distributed to do the test D. Employees at Plant B do not earn more on average compared to employees at Plant A. (d) If the average hourly wage of all workers at Plant B is $14.57, what is the probability of concluding using the decision criteria outlined in part (b) that the mean hourly wage of all employees at Plant B is not greater than the mean hourly wage of all employees at Plant A? Enter your answer to at least three decimals Answer = 0.0170Explanation / Answer
Answer (b): To test the null hypothesis that the two sets of employees get the same wages.
As the company wants to attract new employees by claiming that higher wages are provided in the plant B, the condition which is said to suffice for passing this, will have a t-statistic greater than that required at the alpha significance level.
As we are only looking for "greater than" alternative hypothesis, this is a 1-tailed t-test
t-statistic = (Observed value - Mean/test value ) / ( std. deviation of population/sqrt(sample size) )
=> t = (14.62-13.71)/(2.5/sqrt(38)) = 2.2434 => Looking at t-table to find corresponding alpha value for 1-tailed t-test
Degree of freedom = n-1 = 37
link to t-table: https://www2.palomar.edu/users/rmorrissette/Lectures/Stats/ttests/TTable.jpg
ANSWER (b): alpha = 0.9846 (precise upto 3 decimal places)
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Part (d)
X_new = 14.57 => t-statistic = (14.57-13.71)/(25/(sqrt(38))) = 2.1205
P-value is corresponding to t-score = 2.1205, df = 37 and significance level = 0.9846 => 0.016982 ANSWER (d)