Question

An automobile manufacturer claims that its jeep has a 35.5 miles/gallon (MPG) rating. An independent testing firm has been contracted to test the MPG for this jeep since it is believed that the jeep has an incorrect manufacturer's MPG rating. After testing 140 jeeps, they found a mean MPG of 35.3. Assume the standard deviation is known to be 1.5. A level of significance of 0.1 will be used. Find the value of the test statistic. Round your answer to 2 decimal places.

Enter the value of the test statistic.

Answer 1

Answer 2

Given:

• Claimed MPG (μ₀): 35.5 MPG

• Sample size (n): 140 jeeps

• Sample mean (x̄): 35.3 MPG

• Population standard deviation (σ): 1.5 MPG

• Significance level (α): 0.1

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Step 1: State the Hypotheses

• Null Hypothesis (H₀): The jeep meets the claimed MPG rating.

  $$H_0:\mu =35.5$$

• Alternative Hypothesis (H₁): The jeep does not meet the claimed MPG rating.

  $$H_1:\mu \mathrm{\ne }35.5$$

 Step 2: Calculate the Test Statistic (z-score)

Since the population standard deviation (σ) is known and $n>30$, use the z-test:

$$z=\frac{\bar{x}-{\mu }_0}{\sigma \mathrm{/}\sqrt{n}}$$

Plug in the values:

$$z=\frac{35.3-35.5}{1.5\mathrm{/}\sqrt{140}}=\frac{-0.2}{1.5\mathrm{/}11.83}=\frac{-0.2}{0.127}\approx -1.57$$

Test Statistic:

$$\boxed{{\displaystyle z\approx -1.57}}$$

(Rounded to 2 decimal places.)

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Step 3: Interpret the Result

• Critical z-values for α = 0.1 (two-tailed): ±1.645.

• Since $-1.645<-1.57<1.645$, we fail to reject H₀.

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Conclusion:
There is not enough evidence at the 0.1 significance level to conclude that the jeep’s MPG rating differs from 35.5.