Question

A consumer electronics company is comparing the brightness of two different types of picture tubes for use in its television sets. Tube type A has mean brightness of 100 and standard deviation of 16, and tube type B has unknown mean brightness, but the standard deviation is assumed to be identical to that for type A. A random sample of n=25 tubes of each type is selected, and X_B bar - X_A bar is computed. If μ_B equals or exceeds μA, the manufacturer would like to adopt type B for use. The observed difference is X_B bar - X_A bar=3.0. a.What is the probability that X_B bar exceeds X_A bar by 3.0 or more if μ_B and μ_A are equal? b.Is there strong evidence that μ_Bis greater than μ _{A ?}

Answer 1

Two-Sample T-Test and CI

Method

μ₁: mean of Sample B

µ₂: mean of Sample A

Difference: μ₁ - µ₂

Equal variances are assumed for this analysis.

Descriptive Statistics

Sample	N	Mean	StDev	SE Mean
Sample B	25	103.0	16.0	3.2
Sample A	25	100.0	16.0	3.2

Estimation for Difference

pooled std dev =

Difference	Pooled StDev	95% Lower Bound for Difference
3.00	16.00	-4.59

Test

Null hypothesis	H₀: μ₁ - µ₂ = 0
Alternative hypothesis	H₁: μ₁ - µ₂ > 0

df = n1+n2 - 2 = 25+25-2 = 48.

T-Value	DF	P-Value
0.66	48	0.2553

a.What is the probability that XB bar exceeds XA bar by 3.0 or more if μB and μA are equal?

the probability is p-value = 0.2553

b.Is there strong evidence that μBis greater than μ A ?

considering alpha = 0.05 there is no strong evidence that μBis greater than μ A. because p-value is greater than alpha.