A new diet has been developed for raising beef cows. Two random samples of size

Question

A new diet has been developed for raising beef cows. Two random samples of size nine are independently selected, and one is given the new diet and the other is given the standard diet. After 18 weeks, the weight gain was measured, and it was found that x bar_1 = 30 with s_1 = 8 and x bar_2 = 26 with s_2 = 6. Let mu_1 and mu_2 represent the mean weight gain we would observe for the entire population of beef cows when on, respectively, a new diet and a standard diet. Assume that two-sample t procedures are safe to use. (a) Test the following hypotheses using alpha = 0.01: H_0: mu_1 = mu_2, H_alpha: mu_1 > mu_2 (b) Calculate 95% confidence interval for mu_1 - mu_2.

Explanation / Answer

Folooiwng is the output of t test :

F test shows that p-value is greater than 0.10. That is we can assume that population variances are equal.

So we can use pooled sample t test.

(a)

The t test statistics is

t = 1.20

The p-value is: 0.1238

Since p-value is greater than 0.01 so we fail to reject the null hypothesis.

(b)

The 95% confidence interval is (-3.066, 11.066).

Hypothesis Test: Independent Groups (t-test, pooled variance) X1 X2 30 26 mean 8 6 std. dev. 9 9 n 16 df 4.000 difference (X1 - X2) 50.000 pooled variance 7.071 pooled std. dev. 3.333 standard error of difference 0 hypothesized difference 1.20 t .1238 p-value (one-tailed, upper) -3.066 confidence interval 95.% lower 11.066 confidence interval 95.% upper 7.066 margin of error F-test for equality of variance 64 variance: X1 36 variance: X2 1.78 F .4333 p-value

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