MATH 225N Week 7 Assignment Hypothesis Test for the Meean.

Week 7 Assignment Hypothesis Test for the mean-Polution Standard Deviation known
Compute the value of the test statistic (z-value) for a hypothesis test for one population mean with a
known standard deviation
Question
Jamie, a bowler, claims that her bowling score is less than 168 points, on average.
Several of her teammates do not believe her, so she decides to do a hypothesis
test, at a 1% significance level, to persuade them. She bowls 17 games. The mean
score of the sample games is 155 points. Jamie knows from experience that the
standard deviation for her bowling score is 19 points.
H0: μ≥168; Ha: μ<168
α=0.01 (significance level)
What is the test statistic (z-score) of this one-mean hypothesis test, rounded to two
decimal places?
Provide your answer: Test statistic = -2.82
Correct answers:
 Test statistic = −2.82
The hypotheses were chosen, and the significance level was decided on, so the next
step in hypothesis testing is to compute the test statistic. In this scenario, the
sample mean score, x¯=155. The sample the bowler uses is 17 games,
so n=17. She knows the standard deviation of the games, σ=19. Lastly, the
bowler is comparing the population mean score to 168points. So, this value
(found in the null and alternative hypotheses) is μ0. Now we will substitute the
values into the formula to compute the test statistic:
z0=x¯−μ0σn√=155−1681917√≈−134.608≈−2.82
So, the test statistic for this hypothesis test is z0=−2.82.
Distinguish between one- and two-tailed hypotheses tests and understand possible conclusions
Question
Which graph below corresponds to the following hypothesis test?
H0:μ≥5.9, Ha:μ<5.9
Answer Explanation