MATH 225N Statistics Week 7 Assignment

MATH 225N Statistics Week 7 Assignment 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 168points, 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 17games. The mean score of the sample games is 155points. Jamie knows from experience that the standard deviation for her bowling score is 19points. • H0: μ≥168; Ha: μ168 • 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: The hypotheses were chosen, and the significance level was decided on, so the nextstep in hypothesis testing is to compute the test statistic. In this scenario, the sample mean score, x¯=155. The sample the bowler uses is 17games, so n=17. She knows the standard deviation of the games, σ=19. Lastly, thebowler 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−√≈−134.608≈−2.82 So, the test statistic forthis hypothesis testis 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:μ5.9 AnswerExplanation Correct answer: The alternative hypothesis, Ha, tells us which area of the graph we are interestedin. Because the alternative hypothesis is μ5.9, we are interested in the region less than (to the left of) 5.9, so the correct graph is the first answer choice. Your answer: wrong Identify the null and alternative hypotheses Question A politician claims that at least 68% of voters support a decrease in taxes. A groupof researchers are trying to show that this is not the case. Identify the researchers'null hypothesis, H0, and the alternative hypothesis, Ha, in terms of the parameter p. Select the correct answer below: H0: p≤0.68; Ha: p0.68 H0: p0.68; Ha: p≥0.68 H0: p0.68; Ha: p≤0.68 H0: p≥0.68; Ha: p0.68