a simple random sample of size n=5 is obtained from the population of drivers living in New York City, and the breaking reaction time of each driver is measured. The results are to be used for constructing a 95% confidence interval. What is the number of degrees of freedom that should be used for finding the critical value ta/2?
Degrees of freedom = n - 1
Note: n = sample size
n=5
To find the critical value tα/2, we need to determine the degrees of freedom for the t-distribution.
The formula for degrees of freedom (df) is given by:
df = n - 1
where n is the sample size.
In this case, the sample size (n) is 5. So, the degrees of freedom would be:
df = 5 - 1
= 4
Therefore, the number of degrees of freedom that should be used for finding the critical value tα/2 is 4.
To find the number of degrees of freedom for finding the critical value tα/2, we need to consider the sample size (n) of our random sample.
In this case, the sample size is n = 5. However, the sample size must meet a certain condition in order to use the t-distribution. The condition is that the sample size (n) should be less than or equal to 30.
Since the sample size (n) is 5, which is less than 30, we cannot directly use the t-distribution. Instead, we need to use the small sample approximation, which assumes that the sample follows a normal distribution.
The number of degrees of freedom for the small sample approximation is calculated using the formula (n - 1). Therefore, for a sample size of 5, the number of degrees of freedom should be:
df = n - 1
= 5 - 1
= 4
So, in this case, the number of degrees of freedom to find the critical value tα/2 is 4.