Unit 7 Examples (means t)
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MAT-1430 Business Statistics
Unit 7 Examples (Hypothesis Tests for Means, σ = unknown)
1.
A speaker is trying to make an argument that minimum wage needs to be raised in Pennsylvania. She argues that some companies have reduce hours to less than 32 a week to avoid having to offer benefits and at $7.25 an hour that is not enough to live. To help her argument she took a random sample of 64 part-time employees in different fields to determine if they make less than $230.00 a week (which is less than $12,000.00 a year). She found they make an average of $226.65 with a standard deviation of $10.88. Is this enough evidence to conclude
that part-time employees make less than $230.00 a week? Use a significance level of 0.05.
H0: u=$230
HA: u < $230
N=64
Sample Standard dev=10.88
X=226.65
Df=64-1=63
226.65-230/10.88(squae root(64))=-2.463
T0.05=1.671
[-2.463] > 1.671 Reject H0
Since 2.463 > 1.671, there is enough to suggest the employees are making less than $230 a week
2.
State a Type I and Type II error in the context of the previous exercise.
Type 1 error: concluding that the mean weekly wage is less than $230, when in fact the mean is $230
Type 2 error: Failing to conclude that the mean weekly wage is less than $230 when, in fact the mean is less than $230
3.
A large corporation believes they have very little turnover for employees and the distribution is normally distributed. They have previously concluded that the average employee stays for 7 years. Suppose, of a random sample of 20 employees, they find that the average to be 7.7 years with a standard deviation of 2 years. Comment on the accuracy of the previous conclusion. Use α = 0.01.
H0: u = 7 years
HA: u doesn’t equal 7 years
N=20 employees
X= 7.7 years
S= 2 years
Df= 20-1=19
A=0.01
7.7-7/(2/(square root(20))=1.565
T0.005=2.861
1.565not greater than 2.861 ---Fail to reject H0
Since 1.565 > 2.861, we do not have enough evidence to suggest that the average employee tenure has not changed from 7 years 4.
Check all assumptions and conditions necessary to perform the hypothesis test for the previous exercise.
Randomization Condition: SRS
10% condition: as long as the total # of employees is more than 200, the population is sufficiently large
Independence: One employee’s tenure has no impact on another employee’s tenure
Nearly Normal: the population is normal, so our sampling distribution is normal
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