Question

Today there are some 14 million only children in American families, representing about 20% of all kids, according to the U.S. Census Bureau. A recent survey of 252 Texas State University students shows 13 do not have siblings in their families.

a. Use the survey data to build the 95% confidence interval for population proportion of Texas State students who do not have siblings.

b. Interpret the interval in terms of the problem. Can you safely conclude that percent of bobcat families with one child is significantly smaller than percent of such families in the general population? Explain.

Answer 1

Here we have given that,

n=Total number Texas state university sutdents=252

x: number of Texas state university students shows that they do not have siblings in their families= 13

Now, we estimate the sample proportion as

=sample proportion of Texas state university students shows that they do not have siblings in their families

=

(A)

Now we want to find the 95% confidence interval for the population proportion of Texas State students who do not have siblings p

The formula for CI is as follows,

Now, first, we can find Z-critical value

c=confidence level =0.95

=level of significance= 1-c=1-0.95=0.05

                              =

  = 1.96 Using EXCEL software =ABS(NORMSINV(probability =0.025))

The 95% confidence interval is,

The 95% confidence interval for the population proportion of Texas State students who do not have siblings p is (0.024, 0.079)

(B)

Interpretation:

Here we can say that we are 95 % confident that the population proportion of Texas State students who do not have siblings p will fall inside this interval.

we have given that,

p= population proportion of the of American families representing about kids according to the U.S Census Bureau= 20%=0.20

The 95% CI is (0.024, 0.079)

Here, we can see that the population proportion of p=0.20 is not contained in the interval.

and also we can see that the upper bound of 95% CI is less than p=0.20 hence, we can conclude that the percent of bobcat families with one child is significantly small than percent of such families in the general populaiton.