Question

Twenty years​ ago, 57​% 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 301 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 alpha equals 0.01 level of significance.

Answer 1

Null hypothesis: H0 = 0.57

Alternative hypothesis: Ha ≠ 0.57

z = -11.08

P value = P(Z≠-11.08) = 0.00001

Decision we reject the null hypothesis and accept the alternative hypothesis. That is, parents feel differently today than they did twenty years​ ago

Rule

If;

P-value > significance level --- accept Null hypothesis

P-value < significance level --- reject Null hypothesis

Z score > Z(at 90% confidence interval) ---- reject Null hypothesis

Z score < Z(at 90% confidence interval) ------ accept Null hypothesis

Explanation:

Given;

n=800 represent the random sample taken

Null hypothesis: H0 = 0.57

Alternative hypothesis: Ha ≠ 0.57

Test statistic z score can be calculated with the formula below;

z = (p^−po)/√{po(1−po)/n}

Where,

z= Test statistics

n = Sample size = 800

po = Null hypothesized value = 0.57

p^ = Observed proportion = 301/800 = 0.376

Substituting the values we have

z = (0.376-0.57)/√(0.57(1-0.57)/800)

z = −11.0834525873

z = -11.08

To determine the p value (test statistic) at 0.10 significance level, using a two tailed hypothesis.

P value = P(Z<-11.08) = 0.00001

Since z at 0.10 significance level is between -1.645 and +1.645 and the z score for the test (z = -11.08) which doesn't falls with the region bounded by Z at 0.10 significance level. And also the two-tailed hypothesis P-value is 0.00001 which is lower than 0.10. Then we can conclude that we have enough evidence to FAIL or reject the null hypothesis, and we can say that at 10% significance level the null hypothesis is invalid, therefore we accept the alternative hypothesis.