Question

READ THE DIRECTIONS PLEASE

6) Make your own word problem of the form of this problem. Your word problem should apply directly to biology major. State the null and alternative hypotheses and alpha (α) . (Since you don’t have any data, you need not actually conduct the hypothesis test).

Please make a word problem stated above and answer all the parts based on the question below.

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2 A data set includes data from student evaluations of courses. The summary statistics are n= 90, x 3.59, s=0.66. Use a 0.05 significance level to test the claim that the population of student course evaluations has a mean equal to 3.75. Assume that a simple random sample has been selected. Identify the null and alternative hypotheses, test statistic, P-value, and state the final conclusion that addresses the original claim. (a) Write a and the null and alternative hypotheses. (b) Write the test statistic (indicate whether it is to or zo (c) Identify the critical value (look it up in the attached table) and sketch the rejection region (d) Should we reject Ho or should we fail to reject Ho? (e) Interpret your answer to part (d) within the context of the original problem statement. 7 Repeat problem 6, but make another word problem pertaining to your major. If, in problem 6, the claim to be tested was the null hypothesis Ho, then it should be the alternative hypothesis HA in this problem. Likewise, if, in problem 6, the claim to be tested was the alternative hypothesis HA, then it should be the null hypothesis Ho in this problem TABLE A-3 t Distribution: Critical t Values Left tail Area in One Tail Area in Two Tails Degrees of Critical t value Right tail Critical t value Two tails Critical t value Critical t value POSITIVE z Scores TABLE A-2 (continued) Cumulative Area from the LEFT 5319 5714 6103 5120 5160 5199 5517 6141 6179 6217 6517 0.4 0.5 7019 7454 7486 7517 0.7 7611 8051 8133 8106 0.9 1.0 1.1 1.2 1.3 1.4 1.5 8159 8212 8315 8186 8810 9015 9115 9162 9177 9418 9515 9495 9505 1.7 9616 9713 9812 9817 2.1 ,9911 9913 9916 24 2.5 2.6 2.7 9918 99499951 9972 9974 29 3.50 and up NOTE: For values of zabove 3,.49, use 0.9999 for the area Common Critical Values Confidence Citical ไม่e these cornmon values ful result from interpolation: 0.90 0.95 0.99 1.645 1.96 2575 zScore 1645 0.9500 2575 0.9960

Answer 1

Here we have: a-3.59 S 0.66 n 90 a) α = 0.05 Hypothesis: Hoi 3.75 b) Test statistics: t-distribution (o unknown) 3.59-3.75 0.66 -_ 2.30 V90 t= Vn df = n-1 = 90-1-89

Critical value: tcrit- ta/n df to.os/2,89 1.987 Non rejection Region Rejection Region Rejection Region t-2.30 tc1.987 tc 1.987 P-value 2p (t>l-2.30|) 0.0238 Reject the null hypothesis

e) observed value(-2.30) is less than t-critical value(-1.987), and P-value (0.0238) is less than Alpha value (0.05) We cannot support the claim that the population of student course evaluation has a mean equal to 3.75