Question

The σ population standard deviation is unknown. You collected a simple random sample of the cents portions from 100 checks and from 100 credit card charges. The cents portions of the checks have a mean of 23.8 cents and a standard deviation of 32.0 cents. The cents portions of the credit charges have a mean of 47.6 cents and a standard deviation of 33.5 cents. Use an α = 0.05 level to test the claim that the cents portions of checks have a mean less than that of credit card charges. Using a TI 83/84 calculator, calculate my P-value with the appropriate Hypothesis Test. Use a critical level α = 0.05 and decide to Accept or Reject HO with the valid reason for the decision.

A. My P-value greater than α Alpha, so I Reject Null Hypothesis

B. My P-value greater than α Alpha, so I Accept Null Hypothesis

C. My P-value less than α Alpha, so I Accept Null Hypothesis

D. My P-value less than α Alpha, so I Reject Null Hypothesis

Answer 1

The statistical software output for this problem is:

Two sample Z summary hypothesis test:

μ₁ : Mean of population 1 (Std. dev. = 32)
μ₂ : Mean of population 2 (Std. dev. = 33.5)
μ₁ - μ₂ : Difference between two means
H₀ : μ₁ - μ₂ = 0
H_A : μ₁ - μ₂ < 0

Hypothesis test results:

Difference	n1	n2	Sample mean	Std. err.	Z-stat	P-value
μ1 - μ2	100	100	-23.8	4.6327638	-5.1373222	<0.0001

Hence,

P value is less than alpha so reject null hypothesis.

Option D is correct.