Question

The Survey of Study Habits and Attitudes (SSHA) is a psychological test with scores from 0 to 200. The mean score for U.S. college students is 115. A teacher suspects that older students have better attitudes toward school. She gives the SSHA to an SRS of 45 students from the more 1000 students at her college who are at least 30 years of age. The teacher wants to perform a test at the α = 0.05 significance level of H0: μ = 115 and Ha: μ > 115 where μ = the mean SSHA score in the population of students at her college who are at least 30 years old. Assume the conditions for performing the test are met. In the study of the older students' attitudes, the sample mean SSHA score was 125.7 and the sample standard deviation was 29.8. Use this website to determine the following: a) Calculate the standardized test statistic.

b) Find the P-value.
c) What conclusion can you make?

Answer 1

a: t = 2.21

b: 0.0165

c: we reject the null hypothesis H0: μ = 115 in favor of the alternative hypothesis Ha: μ > 115

Explanation:

a) The standardized test statistic can be calculated as:

t = (sample mean - hypothesized population mean) / (sample standard deviation / sqrt(sample size))

t = (125.7 - 115) / (29.8 / sqrt(45))

t = 2.21

b) To find the P-value, we need to find the area under the t-distribution curve to the right of the calculated t-value with degrees of freedom equal to the sample size minus one (df = 44). We can use a t-distribution table or a calculator with a t-distribution function. For example, using an online calculator with a t-distribution function, we get:

P-value = P(t > 2.21) = 0.0165 (rounded to four decimal places)

c) Since the P-value is less than the significance level α = 0.05, we reject the null hypothesis H0: μ = 115 in favor of the alternative hypothesis Ha: μ > 115. This means that we have evidence to suggest that the mean SSHA score in the population of students at the college who are at least 30 years old is higher than 115. Therefore, the teacher's suspicion that older students have better attitudes toward school is supported by the data.