Question

Homework: 10.2 Save Score: 0 of 1 pt 5 of 8 (6 complote) HW Score: 75%, 6 of 8 pts 10.2.21 Question Help Twenty years ago, 53% 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 294 of 800 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 0.01 level of significance Click here to view the standard normal distribution table (page 1). Click here to view the standard normal distribution table (page 2). 5% of the population size, and the sample the Because npo (1-P) - 10, the sample size is requirements for testing the hypothesis satisfied (Round to one decimal place as needed.)

Answer 1

Solution:

Given:

p = population proportion of children in high school felt it was a serious problem that high school students were not being taught enough math and science

p = 0.53

n = sample size = 800

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

x = 294

We have to test: if parents feel differently today than they did twenty years ago.

Level of significance = 0.01

Part a)

np₀(1-p₀) =800*0.53*(1-0.53) =199.3

Because np₀(1-p₀) =800*0.53*(1-0.53) =199.3 > 10 , the sample size is Less than 5% of the population size and the sample is randomly selected the requirement for testing the hypothesis are satisfied.

Part b) Test the hypothesis:

Step 1) State H0 and H1:

Ho: p=0.53

VS

HP :p +0.53

Step 2) Find test statistic:

-P px(1-P)

where

on = 0.3675

thus

0.3675 -0.53 0.53x(1-0.53) 800

-0.1625 0.53x0.47 800

-0.1625 三,0000311375

-0.1625 0.017646

2 = -9.21

Step 3) Find z critical value:

Level of significance = 0.01

Since this is two tailed test, find

a/2 = 0.01/2 = 0.005

Look in z table for Area = 0.0050 and find corresponding z value.

1.08 .0003 .0014 .0005 .09 .0002 .0003 .0005 .000 2 -3.4 -3.3 -3.2 -3.1 -3.0 -2.9 -2.8 -2.7 -2.6 -2.5 .00 .01 .02 .03 .0003 .0003 .0003 .0003 .0005 .000 .0005 .0004 .0007 .0007 .0006 .0006 .0010 .0009 .0009 .0009 .0013 .0013 .0013 .0012 .0019 .0018 .0018 .0017 .0026 .0025 .0024 .0023 .0035 .0034 .0033 .0032 .0047 .0045 .0044 .0043 005200600050006 .0082 .0080 .0078 .0075 .0107 .0104 .0102 .0099 .0139 .0136 .0132 .0129 .04 .0003 .0004 .0006 .0008 .0012 .0016 .0023 .0031 .0041 .005 .0073 .0096 .0125 .05 .06 .0003 .0003 .0004 .0004 .0006 .0006 .0008 .0008 .0011 .0011 .0016 .0015 .0022 .0021 .0030 .0029 .0040 .0039 .000T005Z .0071 .0069 .0094 .0091 .0122 .0119 .07 .0063 .0004 005 .0008 .0011 .0015 .001 .0018 .0038 .0051 .0068 .0089 .0116 .0015 .001: .0020 .0027 .0037 2.0049 .0066 .0087 .0113 .0007 .0010 .0014 .0019 .0026 .0036 .0048 .0064 .0084 .0110 -2 -2.3 -2.2

Area 0.0050 is in between 0.0049 and 0.0051, and both the area are at same distance from 0.005

thus we look for both area and find both z values.

Area 0.0049 corresponds to -2.5 and 0.08 , thus z= -2.58

Area 0.0051 corresponds to -2.5 and 0.07 , thus z= -2.57

Thus average of both z values is = ( -2.57 + -2.58 ) / 2 = -2.575

Thus critical z value is = -2.575

Since this is two tailed test , there are two z critical values = ( -2.575 , 2.575 )

Step 4) Decision Rule:
Reject null hypothesis ,if z  test statistic value < z critical value = -2.575 or > 2.575 , otherwise we fail to reject H0.

Since z  test statistic value = -9.21 < z critical value = -2.575 ,we reject null hypothesis H0.

Step 5) Conclusion:

Since we have rejected null hypothesis H0, at 0.01 Level of significance, there is sufficient evidence to conclude that parents feel differently today than they did twenty years ago.