Question

section 10.4

Medical research has shown that repeated wrist extension beyond 20 degrees increases the risk of wrist and hand injuries. Each of 24 students at a university used a proposed new computer mouse design. While using the mouse, each student's wrist extension was recorded. Data consistent with summary values given in a paper are given. Use these data to test the hypothesis that the mean wrist extension for people using this new mouse design is greater than 20 degrees. (Use

? = 0.05.

Use a statistical computer package to calculate the P-value. Round your test statistic to two decimal places and your P-value to three decimal places.)

27 26 25 24 27 28 28 25 25 25 28 26

22 28 25 26 27 24 31 28 26 27 27 28

t =

P-value =

Answer 1

Solution:-

State the hypotheses. The first step is to state the null hypothesis and an alternative hypothesis.

Null hypothesis: u < 20
Alternative hypothesis: u > 20

Note that these hypotheses constitute a one-tailed test.  

Formulate an analysis plan. For this analysis, the significance level is 0.05. The test method is a one-sample t-test.

Analyze sample data. Using sample data, we compute the standard error (SE), degrees of freedom (DF), and the t statistic test statistic (t).

SE = s / sqrt(n)

S.E = 0.3798
DF = n - 1

D.F = 23
t = (x - u) / SE

t = 16.78

where s is the standard deviation of the sample, x is the sample mean, u is the hypothesized population mean, and n is the sample size.

The observed sample mean produced a t statistic test statistic of 16.78

Thus the P-value in this analysis is less than 0.00001.

Interpret results. Since the P-value (almost 0) is less than the significance level (0.05), we have to reject the null hypothesis.