Question

Asked Apr 4, 2019

46 views

Step 1

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Step 2

**A.**

**Given information:**

The aim of Cam is to test whether the Albertson’s has lower prices than Ralph’s.

For this he purchases the same basket of foods at five randomly selected Ralph’s stores and eight randomly selected Albertson’s stores. Furthermore, it is said that the price distribution for Albertson’s seems to be skewed right.

*Independent samples:*

Any two randomly selected samples are said to be independent, if the observations in one sample do not depend on the observations in the other sample. In other words it can be said that the observations in one sample should not influence the observations in the other sample.

Here, the two samples Ralph’s stores and Albertson’s stores are random samples. Since, they are selected randomly. The prices of Ralph’s stores do not depend on the prices of Albertson’s stores. That is, observations in Ralph’s stores sample do not influence the observation in Albertson’s stores sample.

Therefore, the two samples Ralph’s stores and Albertson’s stores are independent samples.

The aim is to test whether or not the Albertson’s prices are lower than Ralph’s prices.

Thus, the two independent samples *t *test can be used. Option (b) has to be selected.

Step 3

**Check the validity of the test:**

*Assumptions for two independent samples t test:*

The required conditions for using two independent samples *t *test are given below:

- The two samples must be randomly selected from the two populations.
- The two samples must be independent of one another.
- Population standard deviations must be unknown.
- Either each sample size (
*n*) must be greater than 30 or the populations must be normally distributed.

Here, the sample size of Ralph’s stores prices is *n*1 = 5 and the sample size of Albertson’s stores prices is *n*2 = 8.

Here, both t...

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