You administered a survey to a sample of 442 high school sophomores and found a

Question

You administered a survey to a sample of 442 high school sophomores and found a mean score of 2.3 with a standard deviation of .80. Test the null hypothesis that your sample came from a population in which the mean score is 1.8 against the alternative hypothesis that your sample was drawn from a population with a mean score that is greater than 1.8. Use alpha = .01

Formally state the null and the alternative hypothesis for this test

What is the critical value(s) for this test

What is the critical value(s) for this test

Interpret your decision regarding the null hypothesis

Explanation / Answer

Solution:

Here, we have to use one sample t test for the population means. The null and alternative hypothesis for this test is given as below:

Null hypothesis: H0: The population mean score for high school sophomores is 1.8.

Alternative hypothesis: Ha: The population mean score for high school sophomores is greater than1.8.

H0: µ = 1.8 versus Ha: µ > 1.8

This is a one tailed test. This is an upper tailed or right tailed test.

We are given

Level of significance = = 0.01

Sample size = n = 442

Xbar = 2.3

S = 0.80

df = n – 1 = 442 – 1 = 441

Critical value = 2.3348

(By using t-table or excel)

Test statistic formula is given as below:

Test statistic = t = (Xbar - µ) / [S/sqrt(n)]

Test statistic = t = (2.3 – 1.8)/[0.80/sqrt(442)]

Test statistic = t = (2.3 – 1.8)/ 0.0381

Test statistic = t = 13.1399

P-value = 0.00

(By using t-table or excel)

P-value < = 0.01

So, we reject the null hypothesis that the population mean score for high school sophomores is 1.8.

There is sufficient evidence to conclude that the population mean score for high school sophomores is greater than1.8.

Related Questions

Navigate

• Browse (All)
• Browse Y
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.