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, and while using the mouse, each student's wrist extension was recorded. Data consistent with summary values given in a paper are shown. 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 𝛼 = 0.05.)
25 28 27 24 25 26 26 27 27 27 26 28
22 26 27 28 25 24 31 26 28 25 25 26
(a) State the appropriate null and alternative hypotheses (in degrees). (Enter != for ≠ as needed.)
(b)Find the test statistic. (Round your answer to two decimal places.)
(c) Use technology to find the P-value. (Round your answer to four decimal places.)
Guide On Rating System
Vote
(a) Null hypothesis (H0): The mean wrist extension for people using the new mouse design is equal to 20 degrees.
Alternative hypothesis (Ha): The mean wrist extension for people using the new mouse design is greater than 20 degrees.
(b) To find the test statistic, we will use the one-sample t-test formula:
t = (sample mean - hypothesized mean) / (sample standard deviation / sqrt(sample size))
= (26.42 - 20) / (2.114 / sqrt(24))
= 6.42 / (2.114 / 4.898)
= 6.42 / 0.431
≈ 14.89
The test statistic is approximately 14.89.
(c) Using technology (such as a statistical software or online calculator), we can find the P-value associated with the test statistic. The P-value represents the probability of observing a test statistic as extreme as the calculated one, assuming the null hypothesis is true.
Assuming a t-distribution with 23 degrees of freedom (24 students - 1), a one-sided test (greater than), and a significance level (alpha) of 0.05, the P-value is found to be less than 0.0001.
The P-value is approximately less than 0.0001.
Got a question with my answer?
Cheapmath.com is completely free!
Asking question is free.
Getting answers is free.
+99