Answer:
Critical approach
Since the calculated value is higher than the critical value we have enough evidence to conclude that the true proportion is significantly higher than 0.11 or 11%
P value
We are conducting a right tailed test so then the p value is given by:
And we see that is a very low value compared to the significance level of 0.05 so then we have enough evidence to conclude that the true proportion is significantly higher than 0.11.
Step-by-step explanation:
Information provided
n=1630 represent the random sample selected
X=228 represent the children were found to be living with at least one grandparent
estimated proportion of children were found to be living with at least one grandparent
is the value to verify
represent the significance level
z would represent the statistic
represent the p value
System of hypothesis
We want to verify if the % of children who live with at least one grandparent is higher than 11%, so then the system of hypothesis is .:
Null hypothesis:
Alternative hypothesis:
The statistic for this case is given by:
(1)
Replacing the info given we got:
Critical approach
we need to find a critical value in the normal standard distribution who accumulate 0.05 of the area in the left and for this case this value is:
Since the calculated value is higher than the critical value we have enough evidence to conclude that the true proportion is significantly higher than 0.11 or 11%
P value
We are conducting a right tailed test so then the p value is given by:
And we see that is a very low value compared to the significance level of 0.05 so then we have enough evidence to conclude that the true proportion is significantly higher than 0.11.