Question

An automobile producer wants to estimate the number of miles per gallon (mpg) achieved by its cars. A random sample of 50 cars resulted in a sample mean of 27.6 mpg, and the standard deviation is 2.9 mpg. The producer wants to test the hypothesis that the mean mpg (μ) is not 28.5. Conduct a hypothesis test using a significance level of alpha (α) = 0.05 by providing the following:

(a) The test statistic.
(b) The P-value.
(c) The final conclusion, choosing from the following options:

Answer 1

To test the hypothesis that the mean mpg is not 28.5, we can conduct a Z-test using the sample mean, standard deviation, and sample size. The test statistic is calculated as -2.469, and the p-value is found to be 0.0137. Since the p-value is less than the significance level of 0.05, we reject the null hypothesis and conclude that there is sufficient evidence to support the claim.

Step-by-step explanation:

To conduct a hypothesis test to evaluate the manufacturer's claim, we can use the Z-test since the sample size is large and the population standard deviation is known.

(a) The test statistic is calculated using the formula: Z = (sample mean - hypothesized mean) / (population standard deviation / sqrt(sample size)). Plugging in the values, we get Z = (27.6 - 28.5) / (2.9 / sqrt(50)) = -2.469.

(b) To find the p-value, we can look up the Z-score in the standard normal distribution table or use a statistical calculator. The p-value is the probability of obtaining a test statistic as extreme as or more extreme than the observed value. In this case, the p-value is 0.0137.

(c) Since the p-value (0.0137) is less than the significance level (0.05), we reject the null hypothesis. This means that there is sufficient evidence to support the claim that the mean mpg is not 28.5.