We test H_o: mu lessthanorequalto 0, H_a: mu > 0. Two independent samples of equ

Question

We test H_o: mu lessthanorequalto 0, H_a: mu > 0. Two independent samples of equal size are collected and a z-test with known population standard deviation is performed on each sample. If the mean of the first sample is smaller than the mean of the second sample, which of the following is true? a. If we reject the H_o with sample 2, we should reject the H_o with sample 1. b. If we reject the H_o with sample 1, we should reject the H_o with sample 2. c. If we fail to reject the H_o with both samples, these data must be generated under the H_o. d. If we reject the H_o with both samples, these data must be generated under the H_a. e. If we reject H_o with both samples, these data must be generated under the H_o. For a level alpha = 0.10 t-test for the population mean mu, the null hypothesis is H_o: mu = 0. For a sample of size 16, the sample mean and the sample standard deviation are x = 0.2, and s = 4 respectively. What is the observed value of the t statistic if the population is normally distributed? a. 0.1 b. 0.2 c. equal to t_0 1, 15 d. equal to t_0.1, 9 e. equal to t_0.05, 15 The hypotheses in a z-test for the population mean are H_o: mu lessthanorequalto 1, H_a: mu > 1. For a sample of size 100, the sample mean and the sample standard deviation are x = 2, and s = 10 respectively. Assume alpha = 0.05. Which of the following is the p-value? a. P (Z greaterthanorequalto 1) b. P (Z greaterthanorequalto (1 - 0.2)) c. P (Z greaterthanorequalto z_0.05) d. P (Z lessthanorequalto -z_0.05) e. 1 - P(Z lessthanorequalto 2) Which of the following is true about the conclusions of a significance level alpha hypothesis test? a. If we reject H_o, we might have committed a Type II error

Explanation / Answer

(1)

If H0 is rejected with sample 1, it must also be rejected with sample 2.

(2)

Sample mean, X = 0.2

Sample SD, s = 4

Sample size, n = 16

So, t-statistic = (X-0)/(s/n0.5) = (0.2-0)/(4/160.5) = 0.2

(3)

Sample mean, X = 2

Sample SD, s = 10

Sample size, n = 100

So, z-score = (X-1)/(s/n0.5) = (2-1)/(10/1000.5) = 1

So, the p-value is P(z>= 1)

(4)

If we reject H0 we might have committed a type I error, and if we retain( fail to reject) H0, we might have committed a type II error.

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