We test H_0: mu lessthanorequalto 0, H_a: mu > 0. Two independent samples of equ

Question

We test H_0: mu lessthanorequalto 0, H_a: mu > 0. Two independent samples of equal size are collected and a z-test 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_a with sample 1 b. If we reject H_o with sample 1, we should reject H with sample 2. c. If we to reject the N we both samples, these data must be generated Under the H d If we reject the H with both samples these data must be generated under e we reject H For a level a = 0.10 test for the population mean mu, the null hypothesis H_0: mu = 0. For a sample size 16, the sample mean and the sample standard deviation are r = 0.2, and respectively. What is the observed value of their statistic it the population is normally distributed? a 0.1 b. 0.2 c equal to d. equal to e. equal to The hypotheses in a x-test for the population mean are h: mu lessthanorequalto 1, H_a: mu > 1. For a sample size 100, the sample mean and the sample standard deviation are x = 2, and 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 x_0) d. P(Z lessthanorequalto - x_0) e. (1 - P(Z lessthanorequalto 2) Which of the following is true about the conclusions of a significance level a hypothesis test? a. If we reject might have command a error a type I error

Explanation / Answer

Q.1 Here mean of sample 2 is greater than mean of sample 1 so if we will reject the null hypothesis for sample 1 then it is obvious that we will reject the null hypothesis for sample 2 because it will have high value of test statistic. So, option b is correct.

Q.2 Here test statistic

t = (xbar -0)/(s/sqrt (n)) = 0.2/ (4/sqrt(16) ) = 0.2/ 1 = 0.2

Q.3 xbar =2 and s = 10

alpha = 0.05

Here Z = (xbar - H)/ (s/ sqrt(n)) = (2 -1)/ (10/ sqrt(100)) = 1/1 = 1

so p - value = Pr( Z >1)

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