The average number of miles a person drives per day is 24. A researcher wishes to see if people over age 60 drive less than 24 miles per day. She selects a random sample of 49 drivers over the age of 60 and finds that the mean number of miles per day driven is 22.8. The population standard deviation is 3.5 miles. At a=0.05, is there sufficient evidence that those drivers over 60 years old drive less on average than 24 miles per day? ### Statistical Testing Formula SelectionThis section guides users in selecting the appropriate formula for calculating test values in statistical analyses.**Critical Value (CV) Selection:**- Function: `invNorm`- Round the result to two decimal places.- CV Input Box: For manual entry of the calculated critical value.---**Question: Which formula will we use for the test value?**1. **Option 1:** \[ z = \frac{(\hat{p}_1 - \hat{p}_2) - (p_1 - p_2)}{\sqrt{\hat{p} \cdot \hat{q} \cdot \left( \frac{1}{n_1} + \frac{1}{n_2} \right)}} \]2. **Option 2:** \[ z = \frac{\bar{x} - \mu}{\frac{\sigma}{\sqrt{n}}} \] - **Selected Option:** This option is chosen, indicating it is suitable for the current test context, often used for finding the z-score when population standard deviation is known.3. **Option 3:** \[ t = \frac{\bar{x} - \mu}{\frac{s}{\sqrt{n}}} \]4. **Option 4:** \[ t = \frac{(\bar{x}_1 - \bar{x}_2) - (\mu_1 - \mu_2)}{\sqrt{\frac{s_1^2}{n_1} + \frac{s_2^2}{n_2}}} \]5. **Option 5:** \[ z = \frac{\hat{p} - p}{\sqrt{\frac{p \cdot q}{n}}} \]- **Notes:** - The symbol \(\bar{x}\) represents the sample mean. - The symbol \(\mu\) represents the population mean. - The symbol \(\sigma\) represents the population standard deviation. - The symbol \(s\) represents the sample standard deviation. - \(\hat{p}\) and \(\hat{q}\) are sample proportions. - \(n\) refers to the sample size.A check mark indicates the confirmation of selected option two for this test.

Name: The average number of miles a person drives per day is 24. A researche
Uploaded: 2024-03-20T07:06:16.000Z
Channel: Bartleby
Description: The average number of miles a person drives per day is 24. A researcher wishes to see if people over age 60 drive less than 24 miles per day. She selects a random sample of 49 drivers over the age of 60 and finds that the mean number of miles per day

GIVEN: n=49 Population mean μ=24population standard deviation σ=3.5sample mean x=22.8α=0.05 Hypothesis: H0: μ=24H1: μ<24 Test statistic: z=x-μσn substituting the values in test statistic, z=22.8-243.549 =-1.20.5 =-2.4 P(μ<24)=P(z<-2.4)=0.0082[ which is obtained from excel using "=NORMSDIST(-2.4)"] p value=0.0082 DECISIN RULE: Accept H0, if p value>0.05.CONCLUSION: Since, p value=0.0082 < 0.05, do not accept H0. Thus, it is concluded that, there is sufficient evidence that drivers over 60 years old drive less on average than 24 miles per day.