22. Will is an employee of a cell phone manufacturing company. He is studying battery lifespan as a function of time. He also knows that cell phone battery life varies depending upon usage and habits. All members of this large company are given cell phones. He obtains a list of all employees of the company. He randomly selects 27 employees from this list. He asks them to fully charge their phone, then use it as they usually do for a specified amount of time (hours), then report their battery percentage to him. Here is some computer output from a least-squares regression analysis of the data.
Predictor
Coef
Stdev.
T
P
Constant
96.943
2.369
40.918
0.000
Usage
−7.456
0.361
−20.671
0.000
S = 5.454
R-Sq = 94.5%
R-Sq(adj) = 94.3%
Do these data provide convincing evidence at the = 0.05 level of a negative linear relationship between battery percentage and time (hours) of normal usage in the population of all employees of this company?
STATE:
H0: (b / β ) ( ≠ / > /= / < ) ( 0 / 7.456)
Ha: (b / β ) ( ≠ / > /= / < ) ( 0 / 7.456)
where (b / β ) = the slope of the regression line relating y = battery percentage to x = time (hours) of normal usage in the population of employees of this company using α = 0.05.
PLAN: t test for the slope
Place the phrases in the appropriate boxes.
After placing the phrases, assume the conditions for inference are met and continue to the "DO" step.
Choose from Answer Bank
Linear ____________________________________________
Independent ____________________________________
Normal ___________________________________________
Equal SD ______________________________________
Random _____________________________________
Answer Bank:
a)27 < 10% of all employees of this large company.
b)Check this by examining a histogram of the residuals. Look for no strong skewness or outliers.
c)This is a random sample of 27 employees.
d)Check this by examining the scatterplot. Look for a clear linear pattern.
e)The scatter of points around the residual = 0 line should be the same for all x-values.
DO:
df = ____________________(enter an integer)
= ________________-(Enter 3 decimal places)
P-value = __________________-(Enter 3 decimal places)
CONCLUDE: (choose one option from parenthesis)
Because the P-value (> / < ) α = 0.05, we (reject / fail to reject) . There (is / is not) convincing evidence of a negative linear relationship between battery percentage and time (hours) of normal usage in the population of all employees of this company.
