Question

An experiment was conducted to investigate whether there is a difference in mean bag strengths for two different brands of paper sandwich bags. A random sample of 50 bags from each of Brand X and Brand Y was selected. Each bag was held from its rim, and one-ounce weights were dropped into the bag one at a time from the same height until the bag ripped. The number of ounces the bag held before ripping was recorded, and the mean number of ounces for each brand was calculated.
Which of the following is the appropriate test for the study?

a. A matched-pairs tt-test for a mean difference
b. A two-sample tt-test for a difference between population means
c. A two-sample zz-test for a difference between population proportions
d. A two-sample tt-test for a difference between sample means
e. A one-sample zz-test for a population proportion

Answer 1

Answer:

A two-sample t-test for a difference between sample means

Step-by-step explanation:

Explanation:-

A random sample of 50 bags from each of Brand X and Brand Y was selected

Given two sample sizes n₁ and n₂

Each bag was held from its rim, and one-ounce weights were dropped into the bag one at a time from the same height until the bag ripped

mean of ounces the first sample = x⁻

mean of the  second sample =y⁻

Given data one-ounce weights were dropped into the bag one at a time from the same height until the bag ripped

Standard deviation of the first sample = S₁

Standard deviation of the second sample = S₂

Now we use t - distribution for a difference between the means

$t = \frac{x^{-} -y^{-} }{\sqrt{S^{2}(\frac{1}{n_{1} } +\frac{1}{n_{2} } } }$

where

$S^{2} = \frac{n_{1} S_{1} ^{2} +n_{2}S_{2} ^{2} }{n_{1} +n_{2} -2 }$

Degrees of freedom γ = n₁ +n₂ -2