A rental car charges $25.00 per day plus $.30 for every mile the car is driven. Dale rents a car while his own car is being repa
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We have the following data set:
2,7,15,3,12,9,15,8,3,10
The range is the difference between the highest and lowest values in the set, to find the range, order the data set from least to greatest.
2,3,3,7,8,9,10,12,15,15
Then,
Mean is represented by the following expression:
Population variance formula looks like this:
Then, substituting:
For the standard deviation:
Answer:
The value of the test statistic is
Step-by-step explanation:
Before finding the test statistic, we need to understand the central limit theorem and subtraction of normal variables.
Central Limit Theorem
The Central Limit Theorem establishes 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.
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.
Sample 1:
Sample 2:
The test statistic is:
In which X is the sample mean, is the value tested at the null hypothesis, and s is the standard error.
0 is tested at the null hypothesis:
This means that
Distribution of the difference:
What is the value of the test statistic?
The value of the test statistic is