Questions: A car company claims that its new SUV gets better gas mileage than its competitor's SUV. A random sample of 35 of its SUVS has a mean gas mileage of 16.7 miles per gallon (mpg). The population standard deviation is known to be 0.9 mpg. A random sample of 42 competitor's SUVs has a mean gas mileage of 16.4 mpg. The population standard deviation for the competitor is known to be 0.6 mpg. Test the company's claim at the 0.02 level of significance. Let the car company's SUVs be Population 1 and let the competitor's SUVs be Population 2.

A car company claims that its new SUV gets better gas mileage than its competitor's SUV. A random sample of 35 of its SUVS has a mean gas mileage of 16.7 miles per gallon (mpg). The population standard deviation is known to be 0.9 mpg. A random sample of 42 competitor's SUVs has a mean gas mileage of 16.4 mpg. The population standard deviation for the competitor is known to be 0.6 mpg. Test the company's claim at the 0.02 level of significance. Let the car company's SUVs be Population 1 and let the competitor's SUVs be Population 2.
Transcript text: A car company claims that its new SUV gets better gas mileage than its competitor's SUV. A random sample of 35 of its SUVS has a mean gas mileage of 16.7 miles per gallon (mpg). The population standard deviation is known to be 0.9 mpg. A random sample of 42 competitor's SUVs has a mean gas mileage of 16.4 mpg. The population standard deviation for the competitor is known to be 0.6 mpg. Test the company's claim at the 0.02 level of significance. Let the car company's SUVs be Population 1 and let the competitor's SUVs be Population 2.
failed

Solution

failed
failed
Step 1: State the null and alternative hypotheses
  • Null Hypothesis \(H_0: \mu_1 = \mu_2\)
  • Alternative Hypothesis \(H_a: \mu_1 > \mu_2\)
Step 2: Calculate the test statistic
  • Test Statistic \(Z\) is calculated using the formula: \[Z = \frac{(16.7 - 16.4)}{\sqrt{\frac{\sigma_1^2}{n_1} + \frac{\sigma_2^2}{n_2}}}\]
  • Substituting the values, we get \(Z = 1.685\)
Step 3: Determine the critical value(s)
  • Critical Z-value(s) for a significance level of \(lpha = 0.02\) is/are 2.054
Step 4: Make a decision
  • The test statistic does not fall in the rejection region, thus we fail to reject \(H_0\).
Step 5: Draw a conclusion
  • There is not sufficient evidence to support the claim about the population means.
Was this solution helpful?
failed
Unhelpful
failed
Helpful

Questions asked by other users

failedAnswered
Calculate the volume of O2 under these conditions, in liters: - Pressure: 740 mmHg - Mass: 200 mg - Temperature: 35°C
failedAnswered
2√2 2√2 8√2 9√2
failedAnswered
중요 04 그림은 한 변의 길이가 각각 1 cm, 2 cm, 3 cm 인 정육면체 모 난 후 꺼내 우무 조각의 가운데 부분을 잘랐을 때의 결과이다. 우무 조각을 세포라고 할 때 이 실험 결과를 바탕으로 알 수 있 는 사실로 옳은 것은? (1) 세포의 크기와 물질 교환은 관계가 없다. (2) 세포의 크기가 클수록 표면적의 크기가 작아진다. (3) 세포의 크기가 클수록 부피에 대한 표변적의 비가 키진다. (4) 세포의 크기가 클수록 세포 중심까지 영양소가 흡수되기 에 유리하다. (8) 세포의 크기가 어느 정도 이상 커지면 세포 분열을 하는 것이 물질 교환에 유리하다.
failedAnswered
What is the function of agglutination in antigen-antibody interactions? - Enhance the ease with which pathogens are filtered by the kidneys and spleen - Target and destroy abnormal cells - Prevent the attachment of pathogens and toxins to cells - Kill pathogens that are too large to undergo phagocytosis
failedAnswered
25 of 30 Concepts completed Multiple Choice Question A wheel is free to rotate about a line passing perpendicularly through its center. Only one torque is applied to the wheel. From your point of view (looking along the axis of rotation), the torque causes the wheel to rotate faster in the counterclockwise direction. Identify the direction of the torque exerted on the wheel. Vertically upward Vertically downward Away from you To your right Toward you To your left Need help? Review these concept resources.