Do hardcover and softcover books likely to be found on a professor\'s shelf have
ID: 3272860 • Letter: D
Question
Do hardcover and softcover books likely to be found on a professor's shelf have the same average number of pages? The Minitab output from the "2-sample t" procedure follows. Assume that the books are equivalent to a random sample. (a) Give the null and alternative hypotheses using symbols. H_0: mu_1 - mu_2 0 H_a: mu_1 - mu_2 0 (b) What is the value of the test statistic t? t = (c) Identify the numbers that were used to compute the t-statistic, and verify that the reported value is correct. (Round the answer to two decimal places.) (a - b) - 0/c a = b = c = (d) What conclusion would be made using a .05 level of significance? Write the conclusion in statistical terms and in the context of the problem. the null hypothesis. There is evidence to conclude that the mean number of pages in hardcover books is different from the mean number of pages in softcover books in the population represented by the sample.Explanation / Answer
a. Null hypothesis is the hypothesis of no difference. It is hypothesized that hardcover and softcover books have same mean number of pages. Therefore, the null hypothesis is: H0:mu1-mu2=0 (there is no difference in mean number of pages for hard cover and soft cover pages). The alternative hypothesis states that there is difference in mean number of pages for hard cover and soft cover books. Therefore, the alternative hypothesis is: H1:mu1-mu2=/=0.
H0:mu1-mu2=0
H1:mu1-mu2=/=0
where, 1 denote hard cover and 2 denote soft cover books respectively.
Assume the independent group assumption, independence assumption, randomization condition and nearly normal condition are reasonably met.
The value of test statistic is as follows:
t=(x1bar-x2bar)-(mu1-mu2)/sqrt[s1^2/n1+s2^2/n2], where, xbar denote sample mean, s denote sample standard deviation, n denote sample size.
=(314-436.4)/sqrt[134^2/8+80.9^2/7]
=-2.16
c. a=314; b=436.4; c=sqrt[134^2/8+80.9^2/7]=56.387
d. The p value at 11 degrees of freedom is 0.054. Per rejection rule based on p value, reject null hypothesis is p value is less than alpha=0.05. Here, p value is not less than 0.05, therefore, do not reject null hypothesis. There is insufficient evidence.
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