For the following claim, find the null and alternative hypotheses, test statisti
ID: 3294414 • Letter: F
Question
For the following claim, find the null and alternative hypotheses, test statistic, critical value, and draw a conclusion. Assume that 3 simple random sample has been selected from 3 normally distributed population. Answer parts a-d. Claim: The mean IQ score of statistics professors is less than 125. Sample data: n=27, x= 123, s=4. The significance level is alpha = 0.05. a. Choose the correct null hypothesis (H_0) and alternative hypothesis (H_1). A. H_0: mu 125 B. H_0: mu = 125 H_1: mu notequalto 125 C. H_0: muExplanation / Answer
a. Choose correct hypotheses. Null hypothesis is the hypothesis of no difference. Therefore, it implies that mean IQ score of statistics professor is 125. It is claimed that mean IQ score of statistics professor is less than 125. Therefore, the null and alternative hypotheses are as follows:
H0:mu=125 H1=mu<125 Option D. Option A is wrong as it incorrectly put the claim in the null hypothesis followed by another incorrect claim in the alternative hypothesis.. Option B states the alternative hypothesis to be two tailed test, whereas, it is left-tailed. Option C reversed the null and alternative hypothesis. Thus all three are inappropriate.
b. t=(xbar-mu)/(s/sqrt N), where, xbar is sample mean, mu is population mean, s is sample standard deviation, n is sample size.
=(123-125)/(4/sqrt 27)
=-2.598
c. Using t table, the t critical value at alpha/2=0.025, and n-1=26 degrees of freedom is -2.056.
d. Per rejection rule based on critical value, reject null hypothesis, if observed test statistic falls in critical region. Here, (-2.598>-2.056), thus, reject null hypothesis. Option A and B are discarded. Within C and D, once, you reject null hypothesis, you support the alternative hypothesis. Thus, option C is discarded. Option D is correct.