Question

An engineer is comparing voltages for two types of batteries (K and Q) using a sample of 89 type K batteries and a sample of 103 type Q batteries. The mean voltage is measured as 8.51 for the type K batteries with a standard deviation of 0.312, and the mean voltage is 8.77 for type Q batteries with a standard deviation of 0.779. Conduct a hypothesis test for the conjecture that the mean voltage for these two types of batteries is different. Let μ1 be the true mean voltage for type K batteries and μ2 be the true mean voltage for type Q batteries. Use a 0.05 level of significance. Step 4 of 4 : Make the decision for the hypothesis test.

Answer 1

Two-Sample T-Test and CI

Method

μ₁: mean of type k battries

µ₂: mean of type Q battries

Difference: μ₁ - µ₂

Equal variances are assumed for this analysis.

Descriptive Statistics

Sample	N	Mean	StDev	SE Mean
Sample 1	89	8.510	0.312	0.033
Sample 2	103	8.770	0.779	0.077

Estimation for Difference

Difference	Pooled StDev	95% CI for Difference
-0.2600	0.6090	(-0.4338, -0.0862)

Test

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

T-Value	DF	P-Value
-2.95	190	0.004

Since p-value is less than we reject null hypothesis and we conclude that there is significant difference between the battries.