Question

10 points y=-315.67x + 8986.5 r= -0.951 4,000 3,500 3,000 2,500 car insurance policy cost (dollars) 2.000 1,500 1,000 18 19 20 22 23 24 25 age (years) Every 23-year-old in this group has a lower cost of car insurance than the 18-year- olds. Monthly phone bill cost tends to increase as age of the policyholder increases The value of the correlation coefficient is very close to -1, so there is an association between age and car insurance policy cost The line of best fit indicates that, in general, the cost of the monthly phone bill for a 24-year-old should be on average about $315 less than the cost of a car insurance policy for a 20-year-old. The y-intercept from the line of best fit indicates that if the linear trend holds, the monthly phone bill would be $0 for a person who is about 8.987 years old​

Answer 1

To determine if the mean cost for auto insurance for teenage boys is greater than that for teenage girls, we can perform a t-test. If the test statistic is greater than the critical value, we reject the null hypothesis and conclude that the mean cost for boys is greater.

Step-by-step explanation:

The question asks whether the mean cost for auto insurance for teenage boys is greater than that for teenage girls.

To determine this, we can perform a hypothesis test. We'll use a t-test since we don't know the population standard deviation and have small sample sizes.

1. Null Hypothesis (H0): The mean cost for auto insurance for teenage boys is equal to that for teenage girls (μ1 = μ2)
2. Alternative Hypothesis (H1): The mean cost for auto insurance for teenage boys is greater than that for teenage girls (μ1 > μ2)
3. Significance Level (α): Typically 0.05
4. Test Statistic: t = (x1 - x2) / sqrt((s1^2/n1) + (s2^2/n2)), where x1 and x2 are the sample means, s1 and s2 are the sample standard deviations, and n1 and n2 are the sample sizes
5. Calculate the degrees of freedom using the formula: df = (s1^2/n1 + s2^2/n2)^2 / [(s1^2/n1)^2/(n1-1) + (s2^2/n2)^2/(n2-1)]
6. Find the critical value (tcrit) from the t-distribution table based on the degrees of freedom and significance level
7. Calculate the test statistic t
8. Compare the test statistic t to the critical value tcrit
9. If t > tcrit, reject the null hypothesis and conclude that the mean cost for auto insurance for teenage boys is greater than that for teenage girls
10. If t ≤ tcrit, fail to reject the null hypothesis and conclude that there is not enough evidence to suggest that the mean cost for auto insurance for teenage boys is greater than that for teenage girls

The complete question is:10 points y=-315.67x + 8986.5 r= -0.951 4,000 3,500 3,000 2,500 car insurance policy cost (dollars) 2.000 1,500 1,000 18 19 20 22 23 24 25 age (years) Every 23-year-old in this group has a lower cost of car insurance than the 18-year- olds. Monthly phone bill cost tends to increase as age of the policyholder increases The value of the correlation coefficient is very close to -1, so there is an association between age and car insurance policy cost The line of best fit indicates that, in general, the cost of the monthly phone bill for a 24-year-old should be on average about $315 less than the cost of a car insurance policy for a 20-year-old. The y-intercept from the line of best fit indicates that if the linear trend holds, the monthly phone bill would be $0 for a person who is about 8.987 years old​