1.Build a 95% confidence interval for the population mean wage rate. Show your work, explain your choices. 2.Test H0 that the population mean wage rate is $32/hr, at a 5% significance level. Show your work, explain your choices.3.Given your work in question (2) above, would you be correct to say, “There is sufficient evidence to conclude that the population mean wage rate is below $32/hr?” Explain why or why not. Some critical values you may want to use:ta, df, is the value such that probability P(t > ta, df) = a, where t is a variable that follows a Student'st-distribution with d.f. degrees of freedom: to.025, 7 = 2.365; to.025, 8 = 2.306; to.05,7 = 1.895; to.05, 8 =1.860; to.10, 7 = 1.415; to.10, 8 = 1.397.Za is the value such that probability P(Z > Za) = a, where Z is a variable that follows a standardnormal distribution: Zo.025 = 1.960; Zo.05 = 1.645; Z0.1= 1.282.A researcher went out and collected a random sample of 8 individual wage rates from a populationthat is known to be normally distributed. The wage rates in the sample were:$16/hr, $21/hr, $22/hr, $29/hr, $25/hr, $24/hr, $23/hr, $24/hr.

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1.Build a 95% confidence interval for the population mean wage rate. Show your work, explain your choices.

2.Test H₀ that the population mean wage rate is $32/hr, at a 5% significance level. Show your work, explain your choices.

3.Given your work in question (2) above, would you be correct to say, “There is sufficient evidence to conclude that the population mean wage rate is below $32/hr?” Explain why or why not.

Some critical values you may want to use:
ta, df, is the value such that probability P(t > ta, df) = a, where t is a variable that follows a Student's
t-distribution with d.f. degrees of freedom: to.025, 7 = 2.365; to.025, 8 = 2.306; to.05,7 = 1.895; to.05, 8 =
1.860; to.10, 7 = 1.415; to.10, 8 = 1.397.
Za is the value such that probability P(Z > Za) = a, where Z is a variable that follows a standard
normal distribution: Zo.025 = 1.960; Zo.05 = 1.645; Z0.1= 1.282.
A researcher went out and collected a random sample of 8 individual wage rates from a population
that is known to be normally distributed. The wage rates in the sample were:
$16/hr, $21/hr, $22/hr, $29/hr, $25/hr, $24/hr, $23/hr, $24/hr.

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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