An engineer is comparing voltages for two types of batteries (k and q) using a sample of 37 type k batteries and a sample of 58 type q batteries. the mean voltage is measured as 8.54 for the type k batteries with a standard deviation of 0.225, and the mean voltage is 8.69 for type q batteries with a standard deviation of 0.725. 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 0.10.1 level of significance.
step 1 of 4: state the null and alternative hypotheses for the test.
step 2 of 4: compute the value of the test statistic. round your answer to two decimal places.
step 3 of 4: determine the decision rule for rejecting the null hypothesis h0. round the numerical portion of your answer to two decimal places.
step 4 of 4: make the decision for the hypothesis test.

Step-by-step explanation:

Hello!

You want to test two samples of batteries to see is the mean voltage of these battery types are different.

Sample 1 (type K)

n₁= 37

sample mean x₁[bar]= 8.54

standard deviation S₁= 0.225

Sample 2 (Type Q)

n₂= 58

sample mean x₂[bar]= 8.69

standard deviation S₂= 0.725

1. The test hypothesis are:

H₀: μ₁ = μ₂

H₁: μ₁ ≠ μ₂

2. I'll apply the Central Limit Theorem and approximate the distribution of the sample means to normal so that I can use an approximate Z statistic for this test.

Z: (x₁[bar] - x₂[bar]) - (μ₁ - μ₂) ≈ N(0;1)

        √ (S₁²/n₁) + (S₂²/n₂)

= (8.54 - 8.69) / [√ (0.225²/37) + (0.725²/58)]

= -1.468 ≅ -1.47

3. This is a two tailed test, so you'll have two critical values

You'll reject the null hypothesis if ≤ -1.96 or if ≥ 1.96

You'll not reject the null hypothesis if -1.96 < < 1.96

4.

Since the value = -1.47 is in the acceptance region, the decision is to not reject the null hypothesis.

I hope it helps!

to find the unit price, we must figure out the cost of one item (in this case one dish towel).   to do this, we divide the total price ($7.92) by the number of items bought (for this problem it is 8, because there are eight dish towels in one pack).  

$7.92/8 = $0.99

therefore, the unit price, or the price of one dish towel, is $0.99.

hope this !