Question

1. Seven people were asked to evaluate two different pain relievers, Drug 1 and Drug 2, over a 3-month period and report their effectiveness based on a scale of 1 to 10 (1 being poor” and 10 being "excellent"). The results were Person Drug 1 Drug 2 F G 1 4 Analysts will test the hypotheses that there is a difference in effectiveness between the two drugs. How many degrees of freedom will the test statistic have? A. 2 B. 6 C. 11.9117 D. 12 E. Answer not here 2. Soybean meal is a good source of protein and the amount of amino acid, lvsine, in that meal is an important consideration in its production. A random sample of six soybean meals yielded these lysine measurements 22 g 24 g, 20 g, 26 g 27 g, 25 g. Which of the following shows a plot the p-value (shaded region) for a hypothesis test testing that the population variance is less than 3.68 gº? 9.2393 D. A ffx2) o 9.2393 E. Answn not 3,68 here

Answer 1

1:

Here we have paired data so sample size will be

n=7

The degree of freedom is

df=n-1=6

2:

First we need to fins the mean and SD of data set. Following table shows the calculations:

	X	(X-mean)^2
	22	4
	24	0
	20	16
	26	4
	27	9
	25	1
Total	144	34

Sample size n=6 Sample sum: r=144 Sample mean: X = =144/6 = 24 Sample standard deviation: (x-7) S = Esqrt(34/(6-1)) V n-1 =2.6077 Variance is 52 = E(X=3)*39/(6-1) n-1 =6.8

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Here we have n =6, 52 =6.8 Hypotheses are: H:02 > 3.68 H:02 < 3.68 Level of significance: a =0.05 Test is left tailed. Degree of freedom: df=n-1 =5 Test Statistics: x (0-1) =((6-1)*(6.8)/(3.68) = 9.2391 Critical value(CVs): 1.15 Rejection Region: If x2 < 1.15, Reject HO Decision: Since test statistics does not lie in rejection region so we fail to reject the null hypothesis. P-value: P-value=0.9001 Decision: Since p-value is not less than level of significance so we fail to reject the null hypothesis. Excel function for critical value: Excel function for p-value: ECHIINV(1-0.05,5) = 1-CHIDIST(9.2391,5) Conclusion: That is on the basis of sample evidence we can conclude that populaiton variance is less than 162.

0.20 0.15 0.10 0.05 0.00 | 1.0 3.5 60 8.5 11.0 13.5 16.0