Question

In: Statistics and Probability

The EPA sticker for a particular model of automobile claims the car has average highway mileage...

The EPA sticker for a particular model of automobile claims the car has average highway mileage of 35 miles per gallon. A consumer advocacy group takes a random sample of 30 of these cars and finds that they have an average mileage of 33.6 miles per gallon with a standard deviation of 3 miles per gallon. Do the results of this test provide sufficient evidence to conclude that the actual mileage of this model is less than 35 miles per gallon? Translate this into a statistical hypothesis and carry out the test of hypothesis. Be sure to specify the null and alternative hypotheses, the value of the test statistic, the p-value, and your conclusion.

Solutions

Expert Solution


Related Solutions

A major automobile company claims that its New electric powered car has an average range of...
A major automobile company claims that its New electric powered car has an average range of more that 100 miles. A random sample of 50 new electric cars was selected to test the claim. Assume that the population standard deviation is 12 miles. A 5% level of significance will be used for the test. A) What would be the consequences of making a Type II error in this problem? B) Compute the Probability of making a Type II error if...
A major automobile company claims that its New electric powered car has an average range of...
A major automobile company claims that its New electric powered car has an average range of more than 100 miles. A random sample of 50 new electric cars was selected to test the claim. Assume that the population standard deviation is 12 miles. A 5% level of significance will be used for the test. What would be the consequences of making a Type II error in this problem? Compute the Probability of making a Type II error if the true...
The average gas mileage of a certain model car is 28.0 miles per gallon. If the...
The average gas mileage of a certain model car is 28.0 miles per gallon. If the gas mileages are normally distributed with a standard deviation of 0.4 miles per gallon, find the probability that a car has a gas mileage of between 26.8 and 27.2 miles per gallon.   In addition to the answer, please write out your steps and thoughts that led you to your answer.
A major automobile company claims that its New electric-powered car has an average range of more...
A major automobile company claims that its New electric-powered car has an average range of more than 100 miles. A random sample of 50 new electric cars was selected to test the claim. Assume that the population standard deviation is 12 miles. A 5% level of significance will be used for the test. A) What would be the consequences of making a Type II error in this problem? B) Compute the Probability of making a Type II error if the...
4. In a recent publication, it was reported that the average highway gas mileage of tested...
4. In a recent publication, it was reported that the average highway gas mileage of tested models of a new car was 33.2 mpg with a standard deviation of 2.5 mpg, with the mileages approximately normally distributed. H0 : µ = 33.2 Ha : µ < 33.2 Part a: Describe a Type II error in the context of the hypothesis test. Part b: If a simple random sample of 100 cars is selected, what values of the sample mean ¯x...
4. In a recent publication, it was reported that the average highway gas mileage of tested...
4. In a recent publication, it was reported that the average highway gas mileage of tested models of a new car was 33.2 mpg with a standard deviation of 2.5 mpg, with the mileages approximately normally distributed. H0 : µ = 33.2 Ha : µ < 33.2 Part a: Describe a Type II error in the context of the hypothesis test. Part b: If a simple random sample of 100 cars is selected, what values of the sample mean ¯x...
In a recent publication, it was reported that the average highway gas mileage of tested models...
In a recent publication, it was reported that the average highway gas mileage of tested models of a new car was 33.5 mpg. A consumer group conducts its own tests on a simple random sample of 12 cars of this model and finds that the mean gas mileage for their vehicles is 31.6 mpg with a standard deviation of 3.4 mpg. a) Choose an appropriate significance test for the consumer group to perform to test the publication's assertion. b) The...
In a recent publication, it was reported that the average highway gas mileage of tested models...
In a recent publication, it was reported that the average highway gas mileage of tested models of a new car was 33.2 mpg with a standard deviation of 2.5 mpg, with the mileages approximately normally distributed. H0 :μ=33.2 Ha :μ<33.2 Part a: Describe a Type II error in the context of the hypothesis test. Part b: If a simple random sample of 100 cars is selected, what values of the sample mean x ̄ would represent sufficient evidence to reject...
The highway mileage (mpg) for a sample of 8 different models of a car company can...
The highway mileage (mpg) for a sample of 8 different models of a car company can be found below. 18, 20, 24, 26, 36, 29, 32, 36 Find the 5-number summary, check for any outliers, and use it to create a boxplot.
The highway mileage (mpg) for a sample of 8 different models of a car company can...
The highway mileage (mpg) for a sample of 8 different models of a car company can be found below. Find the mean, median, mode, and standard deviation. Round to one decimal place as needed. 20, 23, 25, 28, 29, 31, 35, 35 Standard Deviation =
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT