A random sample has 49 values. The sample mean is 8.5 and the sample standard deviation is 1.5. Use a level of significance of 0.01 to conduct a left-handed test of the claim that the population mean is 9.2.Is it appropriate to use a Student’s t distribution? How many degrees of freedom do we use?What are the hypotheses?Compute the t value of the sample test statistic.Estimate te P-value for the test.Do we reject or fail to reject the null hypotheses Ho ?Interpret the results.

Name: A random sample has 49 values. The sample mean is 8.5 and the sample
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Description: A random sample has 49 values. The sample mean is 8.5 and the sample standard deviation is 1.5. Use a level of significance of 0.01 to conduct a left-handed test of the claim that the population mean is 9.2.Is it appropriate to use a Student’s t di

Denote μ as the population mean.

Answered: A random sample has 49 values. The…

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A random sample has 49 values. The sample mean is 8.5 and the sample standard deviation is 1.5. Use a level of significance of 0.01 to conduct a left-handed test of the claim that the population mean is 9.2.

Is it appropriate to use a Student’s t distribution? How many degrees of freedom do we use?
What are the hypotheses?
Compute the t value of the sample test statistic.
Estimate te P-value for the test.
Do we reject or fail to reject the null hypotheses H_o ?
Interpret the results.

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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Basic Computation: Testing μ, σ Unknown
A random sample has 49 values. The sample mean is 8.5 and the sample standard deviation is
1.5. Use a level of significance of 0.01 to conduct a left-handed test of the claim that the
population mean is 9.2.
(a) Is it appropriate to use a Student’s t distribution? Explain. How many degrees of
freedom do we use?
(b) What are the hypotheses?
(c) Compute the t value of the sample test statistic.
(d) Estimate the P-value for the test.
(e) Do we reject or fail to reject the null hypotheses H0 ?
(f) Interpret the results.

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