Question

In: Statistics and Probability

A sociologist wants to know about the stress levels in the nation over the past years....

A sociologist wants to know about the stress levels in the nation over the past years. In the late 2000s, the average score on the BSI in the nation was 18 with a variance of 51.84. A current day sample of 28 produces a mean BSI scote of 21.3. What can the sociologist conclude with an a of 0.05?

A) What is the test statistic? One sample t test, independent, z test or related samples t test.

B. What is the population? What is the sample?

C. Compute the test statistic and make a decision about Ho.

E. Compute the effect sizes and magnitude:

r2=

F. Make an interpretation based on results.

There has been a significant increase.

There has been a signigicant decrease

There has been no change.

Solutions

Expert Solution

A) What is the test statistic?

Here, we have to use one sample z test for the population mean, because we are given the value for population standard deviation or variance.

B. What is the population? What is the sample?

The population is all persons in the nation. The sample is 28 randomly selected person.

C. Compute the test statistic and make a decision about Ho.

The null and alternative hypotheses for this test are given as below:

Null hypothesis: H₀: The average score on the BSI in the nation is 18.

Alternative hypothesis: H_a: The average score on the BSI in the nation is greater than 18.

H₀: µ = 18 versus H_a: µ > 18

This is an upper tailed or right tailed (one tailed) test.

The test statistic is given as below:

Z = (Xbar - µ)/[σ/sqrt(n)]

We are given

Xbar = 21.3

σ^2 = 51.84

σ = sqrt(51.84) = 7.2

n = 28

Z = (21.3 – 18)/[7.2/sqrt(28)]

Z = 2.4253

P-value = 0.0076

(by using z-table)

P-value < α = 0.05

So, we reject the null hypothesis H₀

There is sufficient evidence to conclude that the average score on the BSI in the nation is greater than 18.

E. Compute the effect sizes and magnitude:

The formula for effect size is given as below:

d = (Xbar - µ)/σ

d = (21.3 – 18)/7.2

d = 3.3/7.2

d = 0.458333

d ≈ 0.5

There is a medium effect.

F. Make an interpretation based on results.

We reject the null hypothesis and concluded that the average score on the BSI in the nation is greater than 18.There has been a significant increase.

orchestra answered 1 year ago

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