Question

1. A PhD student studying statistics created an hypothesis to generate a p-value. Evaluating the hypothesis ??0: ?? = 0.75 versus ??1: ?? ≠ 0.75, an individual conducting a research , researched 60 randomly selected adults. The information achieved was reflected in a test statistic value of −1.71. What would be the corresponding p-value for this test?

2. A famous shoes place is testing a new shoe line as a new product item at select locations across the country. The company would like to estimate the proportion of customers in these locations that would be pleased with this decision The company wants the estimate to have a margin of error of no more than 3% with 99% confidence. Which minimum sample size needed to obtain the estimate with the desired precision?

a. ) 73

(B) 1842

(C) 1929

(D) Cannot be determined because population standard deviation was not given.

3. A restaurant owner surveyed a random sample of guest who have been to his restaurant the previous year to determine if they were still looking for a job. The survey included 125 who visited and loved the restaurant, of which 15 were still looking for a job. Of the 150 people who hated the restaurant who were surveyed, 12 were still looking for a job. The restaurant owner will use these results to carry out a hypothesis test to investigate whether there is a larger proportion of people who love the restaurant (S) still looking for a job compared to those that hate the restaurant (NS) . 12.

Which of the following is not a condition for carrying out this hypothesis test?

(A) The data come from two independent samples

(B) Both samples were chosen at random

(C) Both populations are normally distributed

(D) Both ??S??̂ S(1 − ??̂ S) and ??NS??̂ NS(1 − ??̂ NS) are more than 10

Which of the following gives the hypotheses for this hypothesis test?

(A) ??0: ??̂ S = ??̂ NS ??1: ??̂ S > ??̂ NS

(B) ??0: ??̂ S > ??̂ NS ??1: ??̂ S = ??̂ NS

(C) ??0: ??S = ??NS ??1: ??S > ??NS

(D) ??0: ??S > ??NS ??1: ??S = ??NS

What is the test statistics for this hypothesis test? ( show work)

Answer 1

(1)

Answer is:

0.0872

Explanation:

Z = - 1.71

Table of Area Under Standard Normal Curve gives area = 0.4564

So,

p - value = (0.5 - 0.4564) X 2 = 0.0872

(2)

Correct option:

(B) 1842

Explanation:

Sample Size (n) is given by:

Given:

= 0.01

From Table, critical values of Z = 2.576

e = 0.03

Since p is not given, Take p = 0.5

Substituting, we get:

(3)

(i)

Correct option:

(C) Both populations are normally distributed

(ii)

Correct option:

(C)   H0: ;   H1:

(iii)

Answer is:

1.11

Explanation:

n1 = 125

= 15/125=0.12

n2 = 150

= 12/150 = 0.08

Test Statistic is given by: