Question

SHOW ALL WORK AND WHICH CALC FUNCTIONS WERE USED

In 1994, 52% of parents with 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 374 of 800 parents with 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 in 1994? Use the α = 0.05 significance level.

a) Determine the null and alternative hypotheses for this scenario.

H0: H1: b) Determine the level of significance.

Answer:
c) Check the assumptions for this problem.

d) Determine the test statistic.

Answer:
e) Determine the p-value.

Answer:
f) Interpret the p-value.

g) What decision do we conclude based on this information? Interpret this in the context of the problem.

Answer 1

Solution:

Given ,

p₀ = 52% = 0.52

Claim : p not equal to p₀

n = 800

x = 374

Use TI83 , 84 , 84 plus calculator.

Steps:

Press STAT

Go to TESTS menu.

Go to 1-PropZTest

p₀: 0.52

x : 374

n : 800

Prop p₀

Calculate

Output:

z = -2.972227215

p = 0.0029566158

a) Determine the null and alternative hypotheses for this scenario.

H0 : p = 0.52

H1 : p   0.52

b) Determine the level of significance.

0.05

c) Check the assumptions for this problem.

n * p = 800 * 0.52 = 416

n * (1 - p ) = 800 * 0.48 = 384

Both are greater than 15. Assumptions met

d) Determine the test statistic.

Answer: -2.972227215

e) Determine the p-value.

Answer: 0.0029566158

f)

p value is less than given level of significance.

So , reject the null hypothesis.

g) What decision do we conclude based on this information?

Reject H0. There is sufficient evidence to support the claim that parents feel differently today than they did in 1994