Hypothesis Testing: Cell Batteries (Math Problem Sample)

Student’s Name
Professor’s Name
MAT 361
Date
Hypothesis Testing I
Q1.
John Kleman is the host of the KXYX Radio AM drive-time news in Denver.
During his morning program, John asked listeners to call in and discuss current
local and national news. This morning, john was concerned with the numbers
of hours children under 12 years of age watched TV per day. The last 5 callers
reported that their children watched the following numbers of hours of hours of
TV last night.
3.0
3.5
4.0
4.5
3.0
Would it be reasonable to develop a confidence interval from these data to
show the mean number of hours of TV watched? If yes, construct an
appropriate confidence interval and interpret the result. If no, why would a
Is the confidence interval not appropriate?
Solution
NO,
We don't have enough data points to determine what the confidence interval (C.I) of the mean is.
Furthermore, calculating and evaluating the Confidence Interval (CI) based on the data points provided would be insignificant for the study.
Q.2
A manufacture of cell phone batteries wants to estimate the useful life of it's
battery (in thousand of hours.) The estimate is to be within 0.10 (100) hours.
Assume a 95% level of confidence and that the standard deviation of the
The useful life of the battery is 0.90 (900 hours). Determine the required sample size.
Solution
We do the correct declaration of variables and see what we have and don't(Nearing et.,al 2020)
C.I = 95%
x_bar = 0.10,
Std =0.9
to calculate confidence interval;
x_bar=z* σ √n
Check for Z_score at 95% CI, from statistical tables, we find Z = 1.96
It Follows;
0.1=1.96× 0.9 √n,
= 100 √n = 0.9 × 1.96 ;
Make n the Subject of the formula;
n=( 0.90×1.96 0.1 ) 2
=311.16≅311
Therefore , we find n is approximately 311
Q3
In a sample of 200 residents of Georgetown country, 120 reported they believe that country real estate taxes were too high. Developed a 95% confidence interval that proportioned of residents who believe the tax rate is too high. Would it be reasonable to conclude that the majority of the taxpayers feel that the tax is too high.
Solution
We know that;
N = 200
Proportion, n = 120
Proportion of people who believe that tax rate is too high,
P = (120/200) =0.60
We wish to perform a test statistic based on the proportion at 95% to see if the proportion falls inside the confidence interval
= 1.96 {p*(1-0.6/120)^0.5}
=0.067896
It is clear that the confidence interval would include the proportion, 0.60, and thus it is significantly adequate to conclude that, YES, the majority of taxpayers believe that taxes are too high.
Q4
The Buffalo distributor wants to find out whether there is a difference in the mean sales for cola stacked at the four locations in the