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 level 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?

58
36
76
66
45
71
47
41
54
96

What are the null and alternative​ hypotheses?

Identify the test statistic.

Identify the critical​ value(

State the final conclusion that addresses the original claim.

▼Fail to reject/Reject Upper H0. There is ▼ not sufficient/sufficient 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?

Answer 1

From the given sample data : n= 10 , ,

The Sample mean is ,

The Sample standard deviation is ,

The null and alternative hypothesis is ,

Vs  

Now , df=degrees of freedom=n-1=10-1=9

The test statistic is ,

The critical value is ,

; From t-table

Decision : Here , the value of the test statistic does not lies in the rejection region.

Therefore , fail to reject tne null hypothesis.

Conclusion : There is not sufficient evidence to support the claim that  the mean number of defined words on a page is greater than 48.0.

Therefore . the results does not suggest that there are more than​ 70,000 defined words in the​ dictionary