Answer:
We conclude that the mean number of residents in the retirement community household is more than or equal to 3.29 persons.
Step-by-step explanation:
We are given that according to the census bureau, 3.29 people reside in the typical american household.
A sample of 16 households in Arizona retirement communities showed the mean number of residents per household was 2.76 residents. the standard deviation of this sample was 1.29 residents.
<u><em>Let </em></u><u><em> = mean number of residents in the retirement community household</em></u>
So, Null Hypothesis, : 3.29 persons {means that the mean number of residents in the retirement community household is more than or equal to 3.29 persons}
Alternate Hypothesis, : < 3.29 persons {means that the mean number of residents in the retirement community household is less than 3.29 persons}
The test statistics that will be used here is <u>One-sample t test statistics</u> as we don't know about population standard deviation;
T.S. = ~
where, = sample mean number of residents per household = 2.76
s = sample standard deviation = 1.29 residents
n = sample of households = 16
So, <u><em>test statistics</em></u> = ~
= -1.643
The value of the test statistics is -1.643.
Now at 0.05 significance level, the <u>t table gives critical value of -1.753 at 15 degree of freedom for left-tailed test</u>. Since our test statistics is more than the critical values of t as -1.643 > 1.753, so we have insufficient evidence to reject our null hypothesis as it will not fall in the rejection region due to which <u>we fail to reject our null hypothesis</u>.
Therefore, we conclude that the mean number of residents in the retirement community household is more than or equal to 3.29 persons.