A manufacturer claims that a particular automobile will get at least 50 miles per gallon on the highway. The researchers at a consumer-oriented magazine plans to test this claim with a simple random sample of 30 cars. Assuming that the standard deviation betweenindividual cars is 2.3 miles per gallon, what should the researchers conclude if the sample mean is 49 miles per gallon?A. There is not sufficient evidence to reject the manufacturer’s claim; 49 miles per gallon is too close to the claimed 50 miles per gallon.B. The manufacturer’s claim should not be rejected because the p-value of 0.0086 is too small.C. The manufacturer’s claim should be rejected because the sample mean is less than the claimed mean.D. The p-value of 0.0086 is sufficient evidence to reject the manufacturer’s claim.Which of the following statements are true?I. If there is sufficient evidence to reject a null hypothesis at the 10% level, then there is sufficient evidence to reject it at the 5% level.II. Whether to use a one- or two-tailed test is typically decided after the data are gathered.III. If a hypothesis test is conducted at the 1% level of significance, there is a 1% chance of rejecting the null hypothesis.A. I only B. III only C. I and III only D. None of the above.A soft drink dispenser can be adjusted to deliver any fixed number of ounces of soft drink. If the machine is operating with a standard deviation of 0.3 ounces, what should the mean setting be so that a 12-ounce cup will overflow less than 1% of the time? Assume a normal distribution for ounces delivered.A. 11.23 oz. B. 11.30 oz. C. 11.70 oz. D. 12.70 oz.When a true null hypothesis is rejected in a hypothesis test, the researcher or analyst hasA. committed a Type I errorB. committed a Type II errorC. made the correct decision.D. to perform the study again.A tire manufacturer claims that its tires have a mean life of at least 50000 km. A random sample of 25 of these tires is tested and the mean life is 33000 km. Suppose the population standard deviation is 2500 km and the lives of tires is approximately normal. To test themanufacturer’s claim at the 5% level of significance, the analyst shouldA. perform a right-tailed test using the t statistic.B. perform a left-tailed test using the t statistic.C. perform a right-tailed test using the z statistic.D. perform a left-tailed test using the z statistic.

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MATLAB: An Introduction with Applications

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A manufacturer claims that a particular automobile will get at least 50 miles per gallon on the highway. The researchers at a consumer-oriented magazine plans to test this claim with a simple random sample of 30 cars. Assuming that the standard deviation between
individual cars is 2.3 miles per gallon, what should the researchers conclude if the sample mean is 49 miles per gallon?
A. There is not sufficient evidence to reject the manufacturer’s claim; 49 miles per gallon is too close to the claimed 50 miles per gallon.
B. The manufacturer’s claim should not be rejected because the p-value of 0.0086 is too small.
C. The manufacturer’s claim should be rejected because the sample mean is less than the claimed mean.
D. The p-value of 0.0086 is sufficient evidence to reject the manufacturer’s claim.
Which of the following statements are true?
I. If there is sufficient evidence to reject a null hypothesis at the 10% level, then there is sufficient evidence to reject it at the 5% level.
II. Whether to use a one- or two-tailed test is typically decided after the data are gathered.
III. If a hypothesis test is conducted at the 1% level of significance, there is a 1% chance of rejecting the null hypothesis.
A. I only B. III only C. I and III only D. None of the above.
A soft drink dispenser can be adjusted to deliver any fixed number of ounces of soft drink. If the machine is operating with a standard deviation of 0.3 ounces, what should the mean setting be so that a 12-ounce cup will overflow less than 1% of the time? Assume a normal distribution for ounces delivered.
A. 11.23 oz. B. 11.30 oz. C. 11.70 oz. D. 12.70 oz.
When a true null hypothesis is rejected in a hypothesis test, the researcher or analyst has
A. committed a Type I error
B. committed a Type II error
C. made the correct decision.
D. to perform the study again.
A tire manufacturer claims that its tires have a mean life of at least 50000 km. A random sample of 25 of these tires is tested and the mean life is 33000 km. Suppose the population standard deviation is 2500 km and the lives of tires is approximately normal. To test the
manufacturer’s claim at the 5% level of significance, the analyst should
A. perform a right-tailed test using the t statistic.
B. perform a left-tailed test using the t statistic.
C. perform a right-tailed test using the z statistic.
D. perform a left-tailed test using the z statistic.

Definition Definition Measure of central tendency that is the average of a given data set. The mean value is evaluated as the quotient of the sum of all observations by the sample size. The mean, in contrast to a median, is affected by extreme values. Very large or very small values can distract the mean from the center of the data. Arithmetic mean: The most common type of mean is the arithmetic mean. It is evaluated using the formula: μ = 1 N ∑ i = 1 N x i Other types of means are the geometric mean, logarithmic mean, and harmonic mean. Geometric mean: The nth root of the product of n observations from a data set is defined as the geometric mean of the set: G = x 1 x 2 ... x n n Logarithmic mean: The difference of the natural logarithms of the two numbers, divided by the difference between the numbers is the logarithmic mean of the two numbers. The logarithmic mean is used particularly in heat transfer and mass transfer. ln x 2 − ln x 1 x 2 − x 1 Harmonic mean: The inverse of the arithmetic mean of the inverses of all the numbers in a data set is the harmonic mean of the data. 1 1 x 1 + 1 x 2 + ...

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