Are my answers below correct Thanks In a survey of 688 US ad

Are my answers below correct? Thanks.

In a survey of 688 US adults with children, 249 of them reported that they saved money for their children’s college education. Can you conclude that more than one third (33%) of US adults with children have saved money for college? Use a 0.05 significance level.

p0 = 0.33

x = 249

n = 688

p1 = x / n = 0.362

a.     State the null (H₀) and alternative (H₁) hypotheses.

H0: p = 0.33

H1: p > 0.33

b.     Give the test statistics and the p-value for this significance test.

Standard Error: (Square Root) (p0 (1 - p0) / n)

(Square Root) (0.33 (1 - 0.33) / 688) = .01793

Test Statistic: z = (p1 - p0) / Standard Error

z = (.362 - .33) / .01793 = 1.785

P_value: = P (Z > 1.785)

= 1 - P (Z < 1.785)

= 1 - .9629 = .0371

c.      Make a decision on whether or not to reject the null hypothesis.

P_value < 0.05, therefore we reject H0

d.     Summarize the conclusion in the context of this problem.

More than 33% of adults have saved money for their children’s college.

Solution

Set Up Hypothesis
Null, H0:P=0.33
Alternate, H1: P>0.33
Test Statistic
No. Of Success chances Observed (x)=249
Number of objects in a sample provided(n)=688
No. Of Success Rate ( P )= x/n = 0.3619
Success Probability ( Po )=0.33
Failure Probability ( Qo) = 0.67
we use Test Statistic (Z) for Single Proportion = P-Po/Sqrt(PoQo/n)
Zo=0.36192-0.33/(Sqrt(0.2211)/688)
Zo =1.7805
| Zo | =1.7805
Critical Value
The Value of |Z | at LOS 0.05% is 1.64
We got |Zo| =1.781 & | Z | =1.64
Make Decision
Hence Value of | Zo | > | Z | and Here we Reject Ho
P-Value: Right Tail - Ha : ( P > 1.78051 ) = 0.0375
Hence Value of P0.05 > 0.0375,Here we Reject Ho

ANS:
More than 33% of adults have saved money for their children’s college