Question

"The Survey of Study Habits and Attitudes (SSHA) is a psychological test that measures the motivation, attitude toward school, and study habits of students. Scores range from 0 to 200, with 200 being the highest level of motivation. The mean score for U.S. college students is about 115, and the standard deviation is about 30. A teacher who suspects that older students have better attitudes toward school gives the SSHA to 30 students who are at least 29 years of age, and their mean was 135.2"
Calculate the observed test statistic (Zobt or Tobt) for hypothesis test. Round up to the second decimal place.

Answer 1

Using the z-distribution, the observed test statistic is given as follows:

z = 3.69.

What are the hypothesis tested?

At the null hypothesis, it is tested if older students have the same mean as the general population, that is:

$H_0: \mu = 115$

At the alternative hypothesis, it is tested if they have a greater mean, that is:

$H_0: \mu > 115$

What is the test statistic?

The test statistic is:

$z = \frac{\overline{x} - \mu}{\frac{\sigma}{\sqrt{n}}}$

In which:

• $\overline{x}$ is the sample mean.

• $\mu$ is the value tested at the null hypothesis.

• $\sigma$ is the standard deviation of the population.

• n is the sample size.

For this problem, the parameters are:

$\overline{x} = 135.2, \mu = 115, \sigma = 30, n = 30$

Hence the test statistic is:

$z = \frac{\overline{x} - \mu}{\frac{\sigma}{\sqrt{n}}}$

$z = \frac{135.2 - 115}{\frac{30}{\sqrt{30}}}$

z = 3.69.

More can be learned about the z-distribution at brainly.com/question/25890103

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