According to a recent publication, the mean price of new mobile homes is $63 comma 800. Assume a standard deviation of $7900.
1 answer:
Answer:
a. For n=25, the mean and standard deviation of the prices of the mobile homes all possible sample mean prices are $63,800 and $1,580, respectively.
b. For n=50, the mean and standard deviation of the prices of the mobile homes all possible sample mean prices are $63,800 and $1,117, respectively.
Step-by-step explanation:
In this case, for each sample size, we have a sampling distribution (a distribution for the population of sample means), with the following parameters:
For n=25 we have:
The spread of the sampling distribution is always smaller than the population spread of the individuals. The spread is smaller as the sample size increase.
This has the implication that is expected to have more precision in the estimation of the population mean when we use bigger samples than smaller ones.
If n=50, we have:
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Answer:
t-value = 2.441
Step-by-step explanation:
Let's assume that this is a one-tailed test to calculate the critical value, the process is this:
- Calculate alpha (α): α = 1 - (confidence level / 100) , but we already have this α=0.01
- Find the critical probability (p*): p* = 1 - α/2 = 1-0.005=0.995
- Then, the critical value would be shown as a t statistic, but for this we need:
degrees of freedom (df)= n-1=35-1=34
- The critical t statistic (t*) or critical value is the t-value having degrees of freedom equal to 34 and a cumulative probability equal to 0.995.
From the attached table we can see:
t-value = 2.441
