1. Michelle purchased 25 audio files in January. In February she
1 answer:
<u>Answer:</u>
Michelle purchased 25 audio files in January. The percent increase is 60%
<u>Solution: </u>
Given Data:
Michelle purchases = 25 audio files in January
Again purchased = 40 audio files in February
We need to find the percent increase for the given data.
Step 1:
Use the formula for percent change ,
Step 2:
First we find the amount of change from the question.
Amount of change = 40 – 25
By subtracting, we get 15.
Step 3:
substitute the values in formula we get,
Formula percent change = = 0.6
Percent = 0.6 100 = 60 %.
Result:
Michelle purchased 25 audio files in January. And In February she purchased 40 audio files. Hence the percent increase is 60%.
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Answer:
a) -6 mpg.
b) 2.77 mpg
c) The 95% confidence interval for the difference of population mean gas mileages for engines A and B and interpret the results, in mpg, is (-8.77, -3.23).
Step-by-step explanation:
To solve this question, we need to understand the central limit theorem, and subtraction of normal variables.
Central Limit Theorem
The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean and standard deviation
, the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean
and standard deviation
.
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
For a proportion p in a sample of size n, the sampling distribution of the sample proportion will be approximately normal with mean and standard deviation
Subtraction between normal variables:
When two normal variables are subtracted, the mean is the difference of the means, while the standard deviation is the square root of the sum of the variances.
Gas mileage A: Mean 36, standard deviation 6, sample of 50:
So
Gas mileage B: Mean 42, standard deviation 8, sample of 50:
So
Distribution of the difference:
Mean:
Standard error:
A. Find the point estimate.
This is the difference of means, that is, -6 mpg.
B. Find the margin of error
We have that to find our level, that is the subtraction of 1 by the confidence interval divided by 2. So:
Now, we have to find z in the Ztable as such z has a pvalue of .
That is z with a pvalue of , so Z = 1.96.
Now, find the margin of error M as such
The margin of error is of 2.77 mpg
C. Construct the 95% confidence interval for the difference of population mean gas mileages for engines A and B and interpret the results(5 pts)
The lower end of the interval is the sample mean subtracted by M. So it is -6 - 2.77 = -8.77 mpg
The upper end of the interval is the sample mean added to M. So it is -6 + 2.77 = -3.23 mpg
The 95% confidence interval for the difference of population mean gas mileages for engines A and B and interpret the results, in mpg, is (-8.77, -3.23).