For this quiz, assume we have a survey of 700 boys and 500 girls. Of those surveyed 4% of the boys watched less than one hour of TV per week, while 7% of the girls watched less than one hour of TV per week. We are testing the claim that the proportion of girls who watch less than one hour of TV per week is greater than that for boys. what is the null and alternate hypothesis?

In this scenario, we are testing whether the proportion of girls who watch less than one hour of TV per week is greater than that of boys.

### Null Hypothesis (H₀):
The null hypothesis states that the proportion of girls who watch less than one hour of TV per week is **equal to or less than** the proportion of boys who watch less than one hour of TV per week.

Mathematically:
\[ H₀: p_g \leq p_b \]

### Alternate Hypothesis (H₁):
The alternate hypothesis states that the proportion of girls who watch less than one hour of TV per week is **greater than** the proportion of boys who watch less than one hour of TV per week.

Mathematically:
\[ H₁: p_g > p_b \]

Where:
- \( p_g \) is the proportion of girls who watch less than one hour of TV per week.
- \( p_b \) is the proportion of boys who watch less than one hour of TV per week.

Would you like to go into the details of hypothesis testing for this scenario? Or do you have any other questions?

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### Relative Questions:

1. How do you calculate the test statistic for comparing two proportions?
2. What significance level (alpha) is typically used in hypothesis testing?
3. How do you interpret the p-value in hypothesis testing?
4. What is the difference between a one-tailed and a two-tailed test?
5. How can you determine if the results of the test are statistically significant?
6. What assumptions must be met for a two-proportion z-test?
7. How do you construct a confidence interval for the difference in proportions?
8. What sample sizes are considered large enough to use the normal approximation in hypothesis testing?

### Tip:
When setting up hypotheses, it's essential to clearly define your null and alternate hypotheses in the context of the research question, as they guide the direction of your statistical test.

Explore hypothesis testing for proportions to compare the percentage of boys and girls watching less than one hour of TV per week. Understand the null and alternate hypotheses, calculate test statistics, and interpret results. Suitable for college-level statistics enthusiasts.

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