Question

Kroger reports that their full time employees make on average 14.50 dollars per hour. You want to examine if the full time employees at the Richmond store are typical of all Kroger employees in terms of income. The Richmond store has 10 full time employees, and you attained their income below. Use a single-sample t-test to determine the outcome (alpha = .05, two-tailed).

Employee 1:   15.75 per hour

Employee 2:   11.75 per hour

Employee 3:   13.75 per hour

Employee 4:   13.50 per hour

Employee 5:   13.50 per hour

Employee 6:   13.50 per hour

Employee 7:   14.75 per hour

Employee 8:   12.50 per hour

Employee 9:   14.00 per hour

Employee 10: 12.00 per hour

provide the following information:

Null Hypothesis in sentence form :

Alternative Hypothesis in sentence form:
Critical Value(s) :

Calculations : Note: the more detail you provide, the more partial credit that I can give you if you make a mistake.

Outcome (determination of significance or not, and what this reflects in everyday language,)

Answer 1

	Samples	Standard Deviation
	15.75	5.063
	11.75	3.063
	13.75	0.063
	13.5	0.000
	13.5	0.000
	13.5	0.000
	14.75	1.563
	12.5	1.000
	14	0.250
	12	2.250
Total	135	13.250
Average	13.5	13.250/9 = 1.472
S	-	1.213

To Test

represent average income of the employees per hour

H₀ : = 14.50 Vs. H₁ = 14.50

H₀ :- The average full time income of employee is $14.50 per hour.

H₁ :- The average full time income of employee is not $14.50 per hour.

Test Statistic:

t = ( ) / ( )

Where, :- Sample Mean

S :- Sample Standard Deviation

n :- Sample Size

t = ( ) / ( )

S² = ( Xi - )² / n-1 = 13.250 / 9 = 1.472

S = = = 1.214

Putting the value of S in the equation we get,

t = (13.5 - 14.5 ) / ( 1.214 / ) = -2.605

Test Criteria :- Reject H₀ if -t < -, n-1

So we have t = -2.605,

-, n-1 = = -2.262

So, -2.605 > -2.262, hence we reject null hypothesis

Decision based on P value

P value = 0.0285

Reject null hypothesis if P-value < = 0.05 (Level of significance)

0.0285 < 0.05, hence we reject the null hypothesis and accept alternative hypothesis.

Conclusion :- Accepting alternative hypothesis,

The average full time income of employee is either greater than $14.50 per hour OR less than $14.50 per hour