Answer:
We conclude that the proportion of families with children under the age of 18 who eat dinner together seven nights a week has increased or remained same.
Step-by-step explanation:
We are given that in a previous poll, 40% of adults with children under the age of 18 reported that their family ate dinner together seven nights a week.
Suppose that, in a more recent poll, 456 of 1194 adults with children under the age of 18 reported that their family ate dinner together seven nights a week.
Let p = <u><em>proportion of families with children under the age of 18 who eat dinner together seven nights a week.</em></u>
SO, Null Hypothesis, : p
40% {means that the proportion of families with children under the age of 18 who eat dinner together seven nights a week has increased or remained same}
Alternate Hypothesis, : p < 40% {means that the proportion of families with children under the age of 18 who eat dinner together seven nights a week has decreased}
The test statistics that would be used here <u>One-sample z test for</u> <u>proportions</u>;
T.S. = ~ N(0,1)
where, = sample proportion of families with children under the age of 18 who eat dinner together seven nights a week =
= 0.38
n = sample of adults = 1194
So, <u><em>the test statistics</em></u> =
= -1.424
The value of z test statistics is -1.424.
<u>Now, at 0.01 significance level the z table gives critical value of -2.326 for left-tailed test.</u>
Since our test statistic is more than the critical value of z as -1.424 > -2.326, 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 proportion of families with children under the age of 18 who eat dinner together seven nights a week has increased or remained same.