Question

Twenty years​ ago, 51​% 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 278 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 0.05 level of significance.

Answer 1

Answer:

Step-by-step explanation:

We would set up the hypothesis test.

For the null hypothesis,

p = 51/100 = 0.51

For the alternative hypothesis,

P ≠ 0.51

Considering the population proportion, probability of success, p = 0.51

q = probability of failure = 1 - p

q = 1 - 0.51 = 0.49

Considering the sample,

Sample proportion, P = x/n

Where

x = number of success = 278

n = number of samples = 800

P = 278/800 = 0.35

We would determine the test statistic which is the z score

z = (P - p)/√pq/n

z = (0.35 - 0.51)/√(0.51 × 0.49)/800 = - 9.05

Recall, population proportion, P = 0.45

The difference between sample proportion and population proportion(p - P) is 0.51 - 0.35 = 0.16

Since the curve is symmetrical and it is a two tailed test, the p for the left tail is 0.51 - 0.16 = 0.35

the p for the right tail is 0.51 + 0.16 = 0.67

These proportions are lower and higher than the null proportion. Thus, they are evidence in favour of the alternative hypothesis. We will look at the area in both tails. Since it is showing in one tail only, we would double the area

From the normal distribution table, the area below the test z score in the left tail is < 0.00001

We would double this area to include the area in the right tail of z = 9.05 Thus

p < 0.00001 × 2

p < 0.00002

Since alpha, 0.01 > than the p value, then we would reject the null hypothesis.

Therefore, at 5% significance level, we can conclude that parents feel differently today than they did twenty years​ ago.