The mean number of sick days an employee takes per year is believed to be about 10. Members of a personnel department do not believe this figure. They randomly survey 8 employees. The number of sick days they took for the past year are as follows: 10; 6; 13; 3; 10; 10; 7; 10. Let X = the number of sick days they took for the past year. Should the personnel team believe that the mean number is about 10? Conduct a hypothesis test at the 5% level1). What is the P value? Explain what the p-value means for this problem.2). Construct a 95% confidence interval for the true mean. Sketch the graph of the situation. Label the point estimate and the lower and upper bounds of the confidence interval. (Round your answers to three decimal places.) A Hypothesis Tests - 1 sample xy! The mean number of sick da XSearch results for ' The mea Xb Answered: A random survey XToday's Christmas Radio I XW Confidence Intervals - MATH X +webassign.net/web/Student/Assignment-Responses/submit?dep=24266164&tags=autosave#Q8Part (f)What is the p-value? (Round your answer to four decimal places.).2190Explain what the p-value means for this problem.O If Ho is true, then there is a chance equal to the p-value that the average number of sick days for employees is at least as different from 10 as the mean of the sample is different from 10.If Ho is false, then there is a chance equal to the p-value that the average number of sick days for employees is at least as different from 10 as the mean of the sample is different from 10.O If Ho is false, then there is a chance equal to the p-value the average number of sick days for employees is not at least as different from 10 as the mean of the sample is different from 10.If Ho is true, then there is a chance equal to the p-value the average number of sick days for employees is not at least as different from 10 as the mean of the sample is different from 10.Incorrect. The interpretation of a p-value is based on the assumption that Ho is true.Part (g)Part (h)Indicate the correct decision ("reject" or "do not reject" the null hypothesis), the reason for it, and write an appropriate conclusion.(i) Alpha (Enter an exact number as an integer, fraction, or decimal.)a = |0.05(ii) Decision:reject the null hypothesisrejectnull hypothesis(iii) Reason for decision:Since a > p-value, we do not reject the null hypothesis.Since a < p-value, we reject the null hypothesis.Since a > p-value, we reject the null hypothesis.Since a < p-value, we do not reject the null hypothesis. A Hypothesis Tests - 1 sample Xy! The mean number of sick da XSearch results for ' The mea Xb Answered: A random survey XToday's Christmas Radio 1 X W Confidence Intervals - MATH x +webassign.net/web/Student/Assignment-Responses/submit?dep=24266164&tags=autosave#Q8(iii) Reason for decision:Since a > p-value, we do not reject the null hypothesis.Since a < p-value, we reject the null hypothesis.Since a > p-value, we reject the null hypothesis.Since a < p-value, we do not reject the null hypothesis.(iv) Conclusion:There is sufficient evidence to conclude that the average number of sick days used per year by an employee is not equal to 10 days.There is not sufficient evidence to conclude that the average number of sick days used per year by an employee is not equal to 10 days.Part (i)Construct a 95% confidence interval for the true mean. Sketch the graph of the situation. Label the point estimate and the lower and upper bounds of the confidence interval. (Round your answers to three decimal places.)95% C.I.2.166.4710.8Additional MaterialsOBook

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MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

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The mean number of sick days an employee takes per year is believed to be about 10. Members of a personnel department do not believe this figure. They randomly survey 8 employees. The number of sick days they took for the past year are as follows: 10; 6; 13; 3; 10; 10; 7; 10. Let X = the number of sick days they took for the past year. Should the personnel team believe that the mean number is about 10? Conduct a hypothesis test at the 5% level

1). What is the P value?

Explain what the p-value means for this problem.

2). Construct a 95% confidence interval for the true mean. Sketch the graph of the situation. Label the point estimate and the lower and upper bounds of the confidence interval. (Round your answers to three decimal places.)

A Hypothesis Tests - 1 sample x
y! The mean number of sick da X
Search results for ' The mea X
b Answered: A random survey X
Today's Christmas Radio I X
W Confidence Intervals - MATH X +
webassign.net/web/Student/Assignment-Responses/submit?dep=24266164&tags=autosave#Q8
Part (f)
What is the p-value? (Round your answer to four decimal places.)
.2190
Explain what the p-value means for this problem.
O If Ho is true, then there is a chance equal to the p-value that the average number of sick days for employees is at least as different from 10 as the mean of the sample is different from 10.
If Ho is false, then there is a chance equal to the p-value that the average number of sick days for employees is at least as different from 10 as the mean of the sample is different from 10.
O If Ho is false, then there is a chance equal to the p-value the average number of sick days for employees is not at least as different from 10 as the mean of the sample is different from 10.
If Ho is true, then there is a chance equal to the p-value the average number of sick days for employees is not at least as different from 10 as the mean of the sample is different from 10.
Incorrect. The interpretation of a p-value is based on the assumption that Ho is true.
Part (g)
Part (h)
Indicate the correct decision ("reject" or "do not reject" the null hypothesis), the reason for it, and write an appropriate conclusion.
(i) Alpha (Enter an exact number as an integer, fraction, or decimal.)
a = |0.05
(ii) Decision:
reject the null hypothesis
reject
null hypothesis
(iii) Reason for decision:
Since a > p-value, we do not reject the null hypothesis.
Since a < p-value, we reject the null hypothesis.
Since a > p-value, we reject the null hypothesis.
Since a < p-value, we do not reject the null hypothesis.

A Hypothesis Tests - 1 sample X
y! The mean number of sick da X
Search results for ' The mea X
b Answered: A random survey X
Today's Christmas Radio 1 X W Confidence Intervals - MATH x +
webassign.net/web/Student/Assignment-Responses/submit?dep=24266164&tags=autosave#Q8
(iii) Reason for decision:
Since a > p-value, we do not reject the null hypothesis.
Since a < p-value, we reject the null hypothesis.
Since a > p-value, we reject the null hypothesis.
Since a < p-value, we do not reject the null hypothesis.
(iv) Conclusion:
There is sufficient evidence to conclude that the average number of sick days used per year by an employee is not equal to 10 days.
There is not sufficient evidence to conclude that the average number of sick days used per year by an employee is not equal to 10 days.
Part (i)
Construct a 95% confidence interval for the true mean. Sketch the graph of the situation. Label the point estimate and the lower and upper bounds of the confidence interval. (Round your answers to three decimal places.)
95% C.I.
2.16
6.47
10.8
Additional Materials
OBook

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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