Question

Assume that a simple random sample has been selected from a normally distributed population and test the given claim. Identify the null and alternative? hypotheses, test? statistic, critical? value(s), and state the final conclusion that addresses the original claim.

A simple random sample of pages from a dictionary is obtained. Listed below are the numbers of words defined on those pages. Given that this dictionary has 1459 pages with defined? words, the claim that there are more than? 70,000 defined words is the same as the claim that the mean number of defined words on a page is greater than 48.0 .Use a 0.01 significance level to test this claim. What does the result suggest about the claim that there are more than? 70,000 defined words in the? dictionary?

57?????37?????51?????70?????54????63?????41?????37????? 67????? 83

What are the null and alternative? hypotheses?

Identify the test statistic.

____ ?(Round to three decimal places as? needed.)

Identify the critical? value(s).

_____ ?(Round to three decimal places as needed. Use a comma to separate answers as? needed.)

State the final conclusion that addresses the original claim.

(Reject, Fail to reject) Ho. There is (sufficient, insufficient) evidence to support the claim that the mean number of defined words is greater than 48.0.

Do the results suggest that there are more than? 70,000 defined words in the? dictionary?

A. There is sufficient evidence to support the claim that there are more than? 70,000 words in the dictionary.

B. The results are inconclusive.

C. Since many pages that were sampled have more than 48? words, there must be more than? 70,000 words in the dictionary.

D. There is not sufficient evidence to support the claim that there are more than? 70,000 words in the dictionary.

Answer 1

Here claim is that the mean number of defined words on a page is greater than 48.0

Which means alternative hypothesis is and null hypothesis is

The t-critical value for a right-tailed test, for a significance level of ?=0.01 is

tc?=2.821

Graphically

Now for the given data sample mean is

and sample mean is

So the test statistics is

As t statistics is not in the reject region we fail to reject the null hypothesis

There is insufficient evidence to support the claim that the mean number of defined words is greater than 48.0.

D. There is not sufficient evidence to support the claim that there are more than? 70,000 words in the dictionary.