x_1 = 32.6 x_2 = 27.8 sigma_1^2 = 89.5 sigma_2^2 = 93.4 n_1 = 25 n_2 = 22 a. Con

Question

x_1 = 32.6 x_2 = 27.8 sigma_1^2 = 89.5 sigma_2^2 = 93.4 n_1 = 25 n_2 = 22 a. Construct a 90% confidence interval for the difference between the population means. (Negative values should be indicated by a minus sign. Round intermediate calculations to 4 decimal places and final answer to 2 decimal places.) b. Specify the competing hypotheses in order to determine whether or not the population means differ. H_0: mu_1 - mu_2 greaterthanorequalto 0: H_A: mu_1 - mu_2 0 H_0: mu_1 - mu_2 = 0: H_A: mu_1 - mu_2 notequalto 0 c. Using the confidence interval from part a, can you reject the null hypothesis? No, since the confidence interval includes the hypothesized value of 0. Yes, since the confidence interval does not include the hypothesized value of 0. Yes, since the confidence interval include the hypothesized value of 0. No, since the confidence interval does not include the hypothesized value of 0.

Explanation / Answer

The statistical software output for this problem is:

Two sample Z confidence interval:
1 : Mean of population 1 (Std. dev. = 9.460444)
2 : Mean of population 2 (Std. dev. = 9.6643675)
1 - 2 : Difference between two means

90% confidence interval results:

Hence,

a) Confidence interval is 0.20 to 9.40

b) Option C is correct.

c) Option B is correct.

Difference n1 n2 Sample mean Std. err. L. limit U. limit 1 - 2 25 22 4.8 2.7974014 0.19868417 9.4013158

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