Question

(8) 8.4.23 Question Hep Assume that a simple random sample has been selected from a normally distríbuted popufation and test the given dlaim Identify the nul and alemativo hypotheses test statistic, crtical values), and state the final conclusion that addresses the original claim A simpla random sampla of pages fom a dictionary pages with d is obtained Listed below are the numbers of words desned on those pages Given that this dictonary has 1459 efined words, the claim that there are more than 70,000 defeed words is the same as the clai m that the mean number of defined words on a page a greater than 48 0 Use a 0 05 level significance level to test this claim. What does the resault sug the dictionary? gest about the clsim that there are more than 70,000 defined worda in 76 47 85 51 53 61 46 50 97 74 Cick the icon to view a table of critical 1 values H480 Identify the test statistic 2827 (Round to three decimal places as needed ) idenitity the criticall value(s) Round to three decimal places as needed Use a cormma to separate answers as needed ) Enter your answer in the answer box and then click check Answer Clear Al emairing

Answer 1

Given that,

Null and alternative hypotheses are,

$H_0: \mu = 48.0$

$H_1: \mu >48.0$

Test statistic is,

$t = \frac {\bar X -\mu}{\frac {s}{\sqrt n}}$

t = 2.827

Since it is right tailed test t-critical value at level of significance $(\alpha)$ = 0.05 with degrees of freedom =n-1=10 -1 =9

is, t-critical value = 1.833

Critical value = 1.833

Here, test statistic = 2.827 > 1.833

=> We reject the null hypothesis H0

Conclusion: There is sufficient evidence to support the claim that the mean number of defined words on a pages is greater than 48.0