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 339 of 850 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 α=0.1 level of significance.Click here to view the standard normal distribution table (page 1). LOADING... Click here to view the standard normal distribution table (page 2). LOADING...Because np01−p0=nothing▼ less than10, the sample size is ▼ less thangreater than 5% of the population size, and the sample ▼ is given to be random,can be reasonably assumed to be random,is given to not be random,cannot be reasonably assumed to be random, the requirements for testing the hypothesis ▼ areare not satisfied.(Round to one decimal place as needed.)

Answer 1

Given data

`\alpha\text{ = 0.1}`

Given claim: proportional difference from 57%

`\begin{gathered} P_o\text{ = 57\% = 0.57} \\ \\ 1-p_o\text{ = }1\text{ - 0.57 = 0.43} \end{gathered}`

Thus,

`\begin{gathered} np_0(1-p_0)=850*0.57*0.43=208.3 \\ \text{Hence, } \\ 208.3>10 \end{gathered}`

The sample size n is the number of parents surveyed from the entire population

`\begin{gathered} n=850 \\ 5\text{ \% of the population }\Rightarrow(5)/(100)*850=0.05*850=42.5 \\ \text{Hence, the sample size > 5 \% of the population size} \end{gathered}`

Since the sample size is greater than 5% of the population, it can be reasonably assumed to be random.

The requirements for testing the hypothesis are satisfied.