Bow Valley College Mean and Standard Deviations Questions

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Mathematics

Bow Valley College

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**Please show all seven steps for each approach. Show your formulas, curves and calculations. **

Question 1. The mean number of sick days an employee takes per year is believed to be about ten. Members of a personnel department do not agree with this figure. They randomly survey eight employees. The number of sick days they took for the past year are as follows: 12; 4; 15; 3; 11; 8; 6; 8. Test the claim at 0.01 level by using both the classical approach and the p-value approach.

Question 2. A poll done for Newsweek found that 13% of Americans have seen or sensed the presence of an angel. A contingent thinks that the percent is less than 13%. It conducts its own survey. Out of 100 Americans surveyed, only seven had seen or sensed the presence of an angel. Conduct a hypothesis test at 0.05 level of significance.

Question 3. A particular brand of tires claims that its deluxe tire averages 50,000 miles before it needs to be replaced. From past studies of this tire, the standard deviation is known to be 8,000. A survey of owners of that tire design is conducted. From the 28 tires surveyed, the mean lifespan was 46,500 miles with a standard deviation of 9,800 miles. Using alpha = 0.05, Conduct a hypothesis test by using both the classical approach and the p-value approach.

Question 4. Registered nurses earned an average annual salary of $69,110. For that same year, a survey was conducted of 41 California registered nurses to determine if the annual salary is higher than $69,110 for California nurses. The sample average was $71,121 with a sample standard deviation of $7,489. Conduct a hypothesis test at 0.05 level by using the classical approach.

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Explanation & Answer

Attached. Please let me know if you have any questions or need revisions.

1.
Data:
Sick days which an employee taken per year
12,4,15,3,11,8,6,8
Mean and standard deviations are calculated using below equations
mean(x̅) =
x̅ =

∑x
N

12 + 4 + 15 + ⋯ + 8
8

x̅ = 8.375
standard deviation(s) = √

∑(x − x̅)2
N−1

∑(x − x̅)2
s =
N−1
2

s=√

(12 − 8.375)2 + (4 − 8.375)2 + ⋯ + (8 − 8.375)2
7

s = 4.1

Step 1
Identifying null and alternative hypothesis
Null hypothesis
The mean number of sick days which an employee taken per year is 10
Alternative hypothesis
The mean number of sick days which an employee taken per year is not 10
H0 : μ = 10
H1 : μ ≠ 10

Step 2
Select the test

As the sample size is less than 30, we have to use t test to test this claim

Step 3
State the level of significance
α = 0.01

Step 4
Calculate the test statistics
t=

t=

x̅ − μ
s/√n
8.375 − 10
4.1/√8

t = −1.12

Step 5
Determination of critical values/p value
Degree of freedom = 7
Since this is a two ...


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