Question

Twenty years​ ago, 52​% of parents of children in high school felt it was a serious problem that high school students were not being taught enough math and science. A recent survey found that 209 of 700 parents of children in high school felt it was a serious problem that high school students were not being taught enough math and science. Do parents feel differently today than they did twenty years​ ago? Use the alpha equals 0.1 level of significance. Click here to view the standard normal distribution table (page 1).LOADING... Click here to view the standard normal distribution table (page 2).LOADING... Because np 0 left parenthesis 1 minus p 0 right parenthesisequals 174.7 greater than ​10, the sample size is less than ​5% of the population​ size, and the sample can be reasonably assumed to be random, the requirements for testing the hypothesis are satisfied. ​(Round to one decimal place as​ needed.) What are the null and alternative​ hypotheses? Upper H 0​: p equals 0.52 versus Upper H 1​: p not equals 0.52 ​(Type integers or decimals. Do not​ round.) Determine the test​ statistic, z 0. z 0equals nothing ​(Round to two decimal places as​ needed.) Determine the critical​ value(s). Select the correct choice below and fill in the answer box to complete your choice. ​(Round to two decimal places as​ needed.) A. z Subscript alphaequals nothing B. plus or minusz Subscript alpha divided by 2equalsplus or minus nothing Choose the correct conclusion below. A. Reject the null hypothesis. There is insufficient evidence to conclude that the number of parents who feel that students are not being taught enough math and science is significantly different from 20 years ago. B. Do not reject the null hypothesis. There is sufficient evidence to conclude that the number of parents who feel that students are not being taught enough math and science is significantly different from 20 years ago. C. Do not reject the null hypothesis. There is insufficient evidence to conclude that the number of parents who feel that students are not being taught enough math and science is significantly different from 20 years ago. D. Reject the null hypothesis. There is sufficient evidence to conclude that the number of parents who feel that students are not being taught enough math and science is significantly different from 20 years ago.

Answer 1

Solution:

Given:

p = 0.52

n = 700

x = Number of parents of children in high school felt it was a serious problem that high school students were not being taught enough math and science

x = 209

Sample proportion is:

level of significance = 0.1

Do parents feel differently today than they did twenty years​ ago?

Part a)

Because np₀(1-p₀) = 700 * 0.52 * (1-0.52) =174.7 > 10 , the sample size is less than ​5% of the population​ size, and the sample can be reasonably assumed to be random, the requirements for testing the hypothesis are satisfied. ​

Part b) What are the null and alternative​ hypotheses?

Part c) Determine the test​ statistic

Part d) Determine the critical​ value(s)

level of significance = 0.1

Since this is two tailed test, find

look in z table for Area = 0.0500 or its closest area and find z value

Area 0.0500 is in between 0.0495 and 0.0505 and both the area are at same distance from 0.0500

Thus we look for both area and find both z values

Thus Area 0.0495 corresponds to -1.65 and 0.0505 corresponds to -1.64

Thus average of both z values is : ( -1.64+ - 1.65) / 2 = -1.645

Thus Z = -1.645 = -1.64

Since this is two tailed test, z critical values are:

Part e)  Choose the correct conclusion below.

Since z test statistic value = -11.73 < z critical = -1.64 , we reject H0.

D) Reject the null hypothesis. There is sufficient evidence to conclude that the number of parents who feel that students are not being taught enough math and science is significantly different from 20 years ago.