A SIMPLE RANDOM SAMPLE OF 47 ADULTS IS OBTAINED FROM A NORMALLY DISTRIBUTED POPU

Question

A SIMPLE RANDOM SAMPLE OF 47 ADULTS IS OBTAINED FROM A NORMALLY DISTRIBUTED POPULATION, AND EACH PERSON'S RED BLOOD CELL COUNT (IN CELLS PER MICROLITER) IS MEASURED. THE SAMPLE MEAN, x = 5.22 AND THE SAMPLE STANDARD DEVIATION, S = 0.55. USE A 0.05 SIGNIFICANCE LEVEL TO TEST THE CLAIM THAT THE SAMPLE IS FROM A POPULATION WITH A MEAN LESS THAN 5.4. A. WHAT ARE THE NULL AND ALTERNATIVE HYPOTHESES? B. IDENTIFY THE TEST STATISTIC (BE SURE TO NOTE IF t OR z). C. STATE THE FINAL CONCLUSION USING P-VALUE OR CRITICAL VALUE. D. WHAT DOES THIS SUGGEST ABOUT THE SAMPLE GROUP? LISTED BELOW ARE AGES OF ACTRESSES AND ACTORS AT THE TIME THEY WON THE AWARD FOR THE CATEGORIES OF BEST ACTRESS OR BEST ACTOR. USE THE SAMPLE DATA TO TEST FO A DIFFERENCE BETWEEN THE AGES OF ACTRESSES AND ACTORS WHEN THEY WON THE AWARD. USE A 0.01 SIGNIFICANCE LEVEL ASSUME THAT THE PAIRED SAMPLE DATA IS A SIMPLE RANDOM SAMPLE AND THAT THE DIFFERENCES HAVE A DISTRIBUTION THAT IS APPROXIMATELY NORMAL A. WHAT ARE THE NULL AND ALTERNATIVE HYPOTHESES? (USE mu_d TO REPRESENT THE MEAN DIFFERENCE IN AGES) B. IDENTIFY THE TEST STATISTIC (BE SURE TO NOTE IF t OR z). C. STATE THE FINAL CONCLUSION USING P-VALUE OR CRITICAL VALUE. D. WHAT DOES THIS SUGGEST ABOUT THE SAMPLE GROUP? YOU CAN USE QUESTION 2 OR 3 AS A BONUS. BE SURE TO INDICATE WHICH IS YOUR BONUS AND WHICH IS TO BE GRADED.

Explanation / Answer

Q.8 Null Hypothesis : H0 : Population mesn is not less than 5.4. >= 5.4

Alternative Hypothesis : Ha : Population mean is less than 5.4 . < 5.4

B. We will use The t test here

Test Statistic

t = (xbar -   H)/ (s/n) = (5.22- 5.40)/ (0.55/ 47) = (-0.18)/ 0.08 = -2.25

C. Here for dF = 47 -1 = 46 and alpha = 0.05 the tcritical = 1.679

so here l t l <  tcritical so we cannot reject the null hypothesis and can conclude that the sample Population mesn is not less than 5.4.

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