In a previous poll, 31% 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, 327 of 1114 adults with children under the age of 18 reported that their family ate dinner together seven nights a week. Is there sufficient evidence that the proportion of families with children under the age of 18 who eat dinner together seven nights a week has decreased? Use the alpha equals α=0.05 significance level.

Question

In a previous poll, 31% 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, 327 of 1114 adults with children under the age of 18 reported that their family ate dinner together seven nights a week. Is there sufficient evidence that the proportion of families with children under the age of 18 who eat dinner together seven nights a week has decreased? Use the alpha equals α=0.05 significance level.

Because np 0 left parenthesis 1 minus- p0 right parenthesis np01−p0equals=238.3238.3

greater than> 10 and the sample size is
less than 5% of the population size, and the sample
can be reasonably assumed to be random,
the requirements for testing the hypothesis
are satisfied.

What are the null and alternative hypotheses?
Upper H0: p equals= 0.31 versus Upper H1: p less than< 0.31

Find the test statistic, z0.
z0equals= −1.19

How do i find the P VALUE given the info
Find the P-value.

Answer 1

To find the p-value, you need to calculate the probability of observing a test statistic as extreme as the one obtained (in this case, -1.19) under the assumption that the null hypothesis is true.

Since the alternative hypothesis is that the proportion has decreased (p < 0.31), you will be conducting a one-tailed test.

To find the p-value, you can use a standard normal distribution table or a calculator.

If you are using a standard normal distribution table, you would find the area in the tail to the left of -1.19. This will give you the probability of getting a test statistic as extreme as -1.19 or less when the null hypothesis is true.

If you are using a calculator, you can use the cumulative distribution function (CDF) of the standard normal distribution. The CDF will give you the probability of getting a test statistic as extreme as -1.19 or less when the null hypothesis is true.

Once you have the p-value, compare it to your significance level (α=0.05). If the p-value is less than α, you can reject the null hypothesis. If the p-value is greater than or equal to α, you do not have enough evidence to reject the null hypothesis.

Please let me know if you need further assistance or have any other questions.