A car company says that the mean gas mileage for its luxury sedan is at least 24 miles per gallon (mpg). You believe the claim is incorrect and find that deviation of 2 mpg. At a=0.10, test the company's claim. Assume the population is normally distributed. Click here to view the t-distribution table Click here to view page 1 of the normal table. Click here to view page 2 of the normal table. n, -24 random sample of 5 cars has a mean gas mileage of 21 mpg and a standard C. H p2 24 O D. Ho us24 H, p> 24 H. p<24 What is the value of the standardized test statistic? The standardized test statistic is -3.35. (Round to two decimal places as needed.) What is the critical value? The critical value is (Round to three decimal places as needed.)

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A car company claims that the mean gas mileage for its luxury sedan is at least 24 miles per gallon (mpg). You doubt the claim and find that a random sample of 5 cars has a mean gas mileage of 21 mpg and a standard deviation of 2 mpg. At a significance level of α = 0.10, test the company's claim. Assume the population is normally distributed.

Links to statistical tables:
- [t-distribution table](#)
- [normal table page 1](#)
- [normal table page 2](#)

Hypotheses:
- \(C \, H_0: \mu \geq 24\)
- \(H_3: \mu < 24\) (Selected option)
- \(D \, H_0: \mu \leq 24\)
- \(H_3: \mu > 24\)

Questions:
1. What is the value of the standardized test statistic?

   **The standardized test statistic is:** -3.35 (Round to two decimal places as needed.)

2. What is the critical value?

   **The critical value is:** [Blank for input] (Round to three decimal places as needed.)

**Explanation of statistical test:**  
This is a one-tailed t-test to determine if the mean gas mileage of the sample is significantly lower than the company's claim of 24 mpg. The test uses the sample mean, standard deviation, and sample size to calculate the test statistic and compare it against the critical value from the t-distribution table.
Transcribed Image Text:A car company claims that the mean gas mileage for its luxury sedan is at least 24 miles per gallon (mpg). You doubt the claim and find that a random sample of 5 cars has a mean gas mileage of 21 mpg and a standard deviation of 2 mpg. At a significance level of α = 0.10, test the company's claim. Assume the population is normally distributed. Links to statistical tables: - [t-distribution table](#) - [normal table page 1](#) - [normal table page 2](#) Hypotheses: - \(C \, H_0: \mu \geq 24\) - \(H_3: \mu < 24\) (Selected option) - \(D \, H_0: \mu \leq 24\) - \(H_3: \mu > 24\) Questions: 1. What is the value of the standardized test statistic? **The standardized test statistic is:** -3.35 (Round to two decimal places as needed.) 2. What is the critical value? **The critical value is:** [Blank for input] (Round to three decimal places as needed.) **Explanation of statistical test:** This is a one-tailed t-test to determine if the mean gas mileage of the sample is significantly lower than the company's claim of 24 mpg. The test uses the sample mean, standard deviation, and sample size to calculate the test statistic and compare it against the critical value from the t-distribution table.
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