Question

Twenty years​ ago, 46​% 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 190 of 750 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.Because

np 0 left parenthesis 1 minus p 0 right parenthesis equals186.3 greater than equals less than not equals greater than

​10,

the sample size is

less than

less than

greater than

​5% of the population​ size, and the sample

can be reasonably assumed to be random,

cannot be reasonably assumed to be random,

can be reasonably assumed to be random,

is given to be random,

is given to not be random,

the requirements for testing the hypothesis

are

are not

are

satisfied.

​(Round to one decimal place as​ needed.)

What are the null and alternative​ hypotheses?

Upper H 0

​:

p

p

mu

sigma

equals

not equals

less than

greater than

equals

. 46versus

Upper H 1

​:

p

p

mu

sigma

not equals

equals

not equals

less than

greater than

. 46

​(Type integers or decimals. Do not​ round.)

Find the test statistic.

z 0

equalsnothing

​(Round to two decimal places as​ needed.)

Find the​ P-value.

​P-valueequals

nothing

​(Round to three decimal places as​ needed.)

Determine the conclusion for this hypothesis test. Choose the correct answer below.

A.

Since

​P-valuegreater than alpha

​,

reject

the null hypothesis and conclude that there

is not

sufficient evidence that parents feel differently today.

B.

Since

​P-valueless than alpha

​,

reject

the null hypothesis and conclude that there

is

sufficient evidence that parents feel differently today.

C.

Since

​P-valueless than alpha

​,

do not reject

the null hypothesis and conclude that there

is

sufficient evidence that parents feel differently today.

D.

Since

​P-valuegreater than alpha

​,

do not reject

the null hypothesis and conclude that there

is not

sufficient evidence that parents feel differently toda

Answer 1

Solution :

Condition :

n = 750 and p_{​​​​​​0} = 0.46

Because np_​​​0(1 - p_{​​​​​​0}) = 186.3, which is 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.

Null and alternative hypotheses :

The null and alternative hypotheses would be as follows :

Test statistic :

To test the hypothesis the most appropriate test is one proportion z-test. The test statistic is given as follows :

Where, p̂ is sample proportion, p is hypothesized value of population proportion under H_{​​​​​​0}, q = 1 - p and n is sample size.

Sample proportion of parents who felt that it was a serious problem that high school students were not being taught enough math and science is given by,

p̂ = x/n

p̂ = (190/750) = 0.2533

n = 750, p = 46% = 0.46 and q = (1 - 0.46) = 0.54

The value of the test statistic is z = -11.36.

P-value :

Since, our test is two-tailed test, therefore we shall obtain two-tailed p-value for the test statistic. The two-tailed p-value is given as follows :

P-value = 2.P(Z > |z|)

We have, |z| = 11.36

P-value = 2.P(Z > 11.36)

P-value = 0.000

The p-value is 0.000.

Conclusion :

Significance level (alpha) = 0.05

P-value = 0.000

(0.000 < 0.05)

Since, p-value is less than alpha, therefore reject the null hypothesis and conclude that there is sufficient evidence that parents feel differently today.

Please rate the answer. Thank you.