6. It. in a sample of n-30 selected from a normal population, x 56 and S 8, what

Question

6. It. in a sample of n-30 selected from a normal population, x 56 and S 8, what is your statistical decision if the level of signficance, a. is 0.10, the rul hypothess, HO, is 50, and the alternative hypotess, Ht-is #50? Determine the critical value(s). The critical value(s) is(are) Round to four decimal places as needed. Use a comma to separate answers as needed.) Determine the test statistic, ISTAT Round to four decimal places as needed.) State your statistical decision·Choose the correct answer below. A. The test does not reject the null hypothesis. The daa provide sumoent evidence to conclude O B. The test repects terul hypothesis. The data provide suficient evidonce to conclude that the O c. The test does not rejot tho null hypothesis The data des not provide sufficient evidence to O D. The test rejects the null hypothesis. The data does not provide sufficient evidence to conclude that the mean differs from -50. mean differs from -50. conclude that the mean differs from u 50. that the mean differs from -50. 3 Table of critical values of t (page 1) Critical Values of t For a particular number of degrees of freedom, entry represents the critical value of t corresponding to the cumwlative probability (I - a) and a specified upper-tail area(a). Cumulative Probabilities 0.90 0.95 0.975 0.99 0.995 Upper-Tail Areas Degrees of 0.025 0,01 0.005 3.0777 1.8856 1.6377 15332 2.1318 14759 6.3138 2.9200 2.3534 31.8207 6.9646 12.7062 63.6574 1.0000 0.8165 0.7649 0.7407 0.7267 0.7176 2.0150 1.9432 1.8946 1.8595 18331 1.8125 1.7959 1.7823 4.3027 3.1824 2.7764 2.5706 2.4469 2.3646 2.3060 2.2622 2.2281 2.2010 2.1788 4.5407 3.7469 3.3649 .1427 2.9980 2.8965 2.8214 2.7638 2.7181 2.6810 2.6503 9.9248 5.8409 4.6041 4.0322 3.7074 3.4995 3.3554 14398 14149 13968 1.3830 0.7064 0.7027 0.69981.3722 3.2498 3.1693 3.1058 3.0545 10 0.6974 0.6955 1.3634 1.3562 12 13 0.6938 1.3502 1.7709 2.1604 sxlitemprod pearsoncmg.com/apiv1/printimath

Explanation / Answer

for 0.1 level and (30-1=29) degree of freeedom and for two tailed test crtiical value =-1.70 ; 1.70

here std error of mean =std deviation/(n)1/2 =8/(30)1/2 =1.4606

tstat =(X-mean)/std error =(56-50)/1.4606=4.1079

option B is correct

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