Question

a survey found that in a sample of 100 families, 30 owned dogs ( ). another survey, done 15 years ago, found that in a sample of 60 families, 30 owned dogs ( ). at a 0.10 level of significance, has the proportion of dog owners changed over the 15-year period? a) which are the null and alternative hypotheses?

Answer 1

The null and alternative hypotheses for this study are as follows: Null Hypothesis (H0): The proportion of dog owners has not changed over the 15-year period. Alternative Hypothesis (Ha): The proportion of dog owners has changed over the 15-year period. To test whether the proportion of dog owners has changed, perform a hypothesis test using the given data and a significance level of 0.10.

Step-by-step explanation:

The null and alternative hypotheses for this study can be defined as follows:

• Null Hypothesis (H0): The proportion of dog owners has not changed over the 15-year period.
• Alternative Hypothesis (Ha): The proportion of dog owners has changed over the 15-year period.

To test whether the proportion of dog owners has changed, you can perform a hypothesis test using the given data and a significance level of 0.10. This can be done by calculating the test statistic using the formula:

test_statistic = (p2 - p1) / sqrt(p * (1 - p) * (1/n1 + 1/n2))

where p1 and p2 are the proportions of dog owners in the two surveys, p is the pooled proportion, and n1 and n2 are the sample sizes. If the test statistic falls in the rejection region, you can reject the null hypothesis and conclude that the proportion of dog owners has changed over the 15-year period.