In each of the following scenarios, determine if the data are paired.

1. We would like to know if Intel's stock and Southwest Airlines' stock have similar rates of return. To find out, we take a random sample of 50 days for Intel's stock and another random sample of 50 days for Southwest's stock.

a. Paired
b. Not Paired

2. We randomly sample 50 items from Target stores and note the price for each. Then we visit Walmart and collect the price for each of those same 50 items.

a. Paired
b. Not Paired

3. A school board would like to determine whether there is a difference in average SAT scores for students at one high school versus another high school in the district. To check, they take a simple random sample of 100 students from each high school.

a. Paired
b. Not Paired

Answer:

1. Can be Paired or Not Paired

2. Paired

3. Not Paired

Step-by-step explanation:

Two sets of observations are paired if each observation in one set has a special correspondence or connection with exactly one observation in the other data set.

1. Can be Paired or Not paired

Reason -

We might look at testing the difference of means using a two sample t-test. However, we may also try running a paired t-test.

But its used in cases where the observations are usually from the same populations at different times or through different sources etc.

Hence can't conclude that it is paired or not paired.

2. Paired

Reason -

Each record is a price of the same item from different stores.

3. Not paired

Reason -

This is again a case of testing the difference of means of two-samples (2 independent samples precisely) that are not paired.

1. Can't conclude paired or not paired

2. Paired

3. Not Paired

Two sets of observations are said to be paired if each observation in one data set has a specific connection with exactly one observation in the other data set otherwise it is unpaired.

1. Can't conclude paired or not paired because It may look at testing the difference of means using a two-sample test, But it's used in cases where the observations are from the same populations at different times or through various sources, etc.

2. Paired because each item is the price of the same item from different stores.

3. Not paired because in this case of testing the difference of means of two independent samples that are not paired.

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