The work week for adults in the US that work full time is normally distributed with a mean of 47 hours. A newly hired engineer at a start-up company believes that employees at start-up companies work more on average then most working adults in the US. She asks 12 engineering friends at start-ups for the lengths in hours of their work week. Their responses are shown in the table below. Test the claim using a 5% level of significance. Give answer to at least 4 decimal places. Hours 50 40 57 55 46 62 51 60 46 50 51 54 (a) Determine the null and alternative hypotheses? H0: Select an answer s x̄ σ² s² σ p̂ μ p ? < = ≠ ≥ ≤ > hours H1: Select an answer σ² x̂ s² s p̂ μ p σ ? = < ≠ > ≥ ≤ hours (b) Determine the test statistic ? t= z= (c) Determine the p-value. p-value = (d) Make a decision. Do not reject the null hypothesis Accept the null hypothesis Accept the alternative hypotheis Reject the null hypothesis (e) The correct conclusion would be: There is not sufficient evidence to support the claim the mean number of hours of all employees at start-up companies work more than the US mean of 47 hours There is not sufficient evidence to support the claim that the mean number of hours of all employees at start-up companies work the US mean of 47 hours There is sufficient evidence to support the claim that the mean number of hours of all employees at start-up companies work the US mean of 47 hours There is sufficient evidence to support the claim that the mean number of hours of all employees at start-up companies work more than the US mean of 47 hours

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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The work week for adults in the US that work full time is normally distributed with a mean of 47 hours. A newly hired engineer at a start-up company believes that employees at start-up companies work more on average then most working adults in the US. She asks 12 engineering friends at start-ups for the lengths in hours of their work week. Their responses are shown in the table below. Test the claim using a 5% level of significance. Give answer to at least 4 decimal places.

Hours
50
40
57
55
46
62
51
60
46
50
51
54

(a) Determine the null and alternative hypotheses?

H₀: Select an answer s x̄ σ² s² σ p̂ μ p ? < = ≠ ≥ ≤ > hours

H₁: Select an answer σ² x̂ s² s p̂ μ p σ ? = < ≠ > ≥ ≤ hours

(b) Determine the test statistic ? t= z=

(c) Determine the p-value. p-value =

(d) Make a decision.

Do not reject the null hypothesis
Accept the null hypothesis
Accept the alternative hypotheis
Reject the null hypothesis

(e) The correct conclusion would be:

There is not sufficient evidence to support the claim the mean number of hours of all employees at start-up companies work more than the US mean of 47 hours
There is not sufficient evidence to support the claim that the mean number of hours of all employees at start-up companies work the US mean of 47 hours
There is sufficient evidence to support the claim that the mean number of hours of all employees at start-up companies work the US mean of 47 hours
There is sufficient evidence to support the claim that the mean number of hours of all employees at start-up companies work more than the US mean of 47 hours

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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