TIME WASTED AT WORK? An employment survey at a local small business was conducted to see how much time is wasted at work by employees during an 8-hour workday. Below are the results of a random sample of 10 employees employed at this small business who were asked to truthfully and anonymously record how much time in minutes is wasted in an 8-hour workday. The owner of the small business claims less than 115 minutes is wasted in an 8-hour workday. Does this data provide evidence to support the claim that employees waste less than 115 minutes in an 8-hour workday at α=.05? 108 112 117 130 111 131 113 113 105 128 Demonstrate this sample came from an approximately normal population by producing a graph. (Histogram, boxplot, dot plot or stem plot) Copy and paste your graph here. Is this a test for a population proportion or a population mean? What distribution is used to conduct this test? Is this a left-tailed, right-tailed, or two-tailed test? State AND verify all assumptions required for this test. [HINT: This test should have two assumptions to be verified.] State the null and alternate hypotheses for this test: (use correct symbols and format!) Null hypothesis : : Alternate hypothesis : : Run the correct hypothesis test and provide the information below. Give the correct symbols AND numeric value of each of the following (round answers to 3 decimal places). Test Statistic: Critical value [HINT: this is NOT ] : Degrees of freedom: p-value : State your statistical decision (Justify it using the p-value or critical value methods!) and interpret your decision within the context of the problem. What is your conclusion?

An employment survey at a local small business was conducted to see how much time is wasted at work by employees during an 8-hour workday. Below are the results of a random sample of 10 employees employed at this small business who were asked to truthfully and anonymously record how much time in minutes is wasted in an 8-hour workday. The owner of the small business claims less than 115 minutes is wasted in an 8-hour workday. Does this data provide evidence to support the claim that employees waste less than 115 minutes in an 8-hour workday at α=.05?

108	112	117	130	111
131	113	113	105	128

Demonstrate this sample came from an approximately normal population by producing a graph. (Histogram, boxplot, dot plot or stem plot) Copy and paste your graph here.

Is this a test for a population proportion or a population mean?
What distribution is used to conduct this test?
Is this a left-tailed, right-tailed, or two-tailed test?

State AND verify all assumptions required for this test.

[HINT: This test should have two assumptions to be verified.]

State the null and alternate hypotheses for this test: (use correct symbols and format!)

Null hypothesis : :

Alternate hypothesis : :

Run the correct hypothesis test and provide the information below. Give the correct symbols AND numeric value of each of the following (round answers to 3 decimal places).

Test Statistic:

Critical value [HINT: this is NOT ] :

Degrees of freedom:

p-value :

State your statistical decision (Justify it using the p-value or critical value methods!) and interpret your decision within the context of the problem. What is your conclusion?

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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