Null Hypothesis test

Question

In a large scale study done 10 years ago 32% of adults with children under the age of 18 reported that their family ate dinner together seven nights a week in a recent pole 175 of 500 adults with children under 18 reported that their family ate dinner together seven nights a week do these results indicate the proportion of families with children under 18 who eat dinner together seven nights a week has changed significantly?

X=______________________ nl_

H_o:

_Ha:

_{p-value work space :}

_conclusion:

_{what type of error are you in danger of having made?}

Answer 1

In a large scale study done 10 years ago 32% of adults with children under the age of 18 reported that their family ate dinner together seven nights a week in a recent pole 175 of 500 adults with children under 18 reported that their family ate dinner together seven nights a week do these results indicate the proportion of families with children under 18 who eat dinner together seven nights a week has changed significantly?

Answer:

Part 1:

We can model this problem with a binomial distribution where,

Y = 175

n = 500

and p=0.32 since we have the study done 10 years ago 32% of adults had dinner together.

The model is that such a pole will generate a random number that follows,

X ~ Binomial( 500, 0.32)

Part 2:

Now, since this 32% is the base truth, this will be our Null.

H0 : p = 0.32

Ha: p ≠ 0.32

Part 3:

Since, Y = 175

We have to find the probability of a number 175 or more occurring in such pole.

In math, P(Y >= 175)

Using Binomial table, we can see that

P(Y >= 175) = 0.083

So, our p-value is 0.083

Part 4:

Our common consensus is to have a p-value less than 0.05 to reject the Null Hypothesis.

So, we can not reject the null hypothesis.

It means that it hasn't changed significantly.