Question

A researcher is studying the amount of living space of households in apartments in Kitchener-Waterloo. Suppose the true distribution of the square footage, X, follows a normal distribution, X~N(800,10,000).How probable would it be that the researcher obtains a sample varianceless than 6400 if they draw random samples of size n = 30?You can either use table 7b to bound this probability, or use the formula “=CHISQ.DIST.RT(x, degrees of freedom)”to find an exact value in Excel.

Answer 1

In this case, n = 30, s² = 6400, σ² = 10000

X² = (30-1)*6400/10000 = 18.56

Now, we have to find P(X² < 18.56)

P(X² < 18.56) = 1 - P(X²> 18.56)

The, value of P(X²> 18.56) can be found using the excel function =CHISQ.DIST.RT(x, degrees of freedom)

In this case, x = 18.56 and Degrees of freedom = n-1 = 30-1 = 29

Using excel, we found P(X²> 18.56) = 0.9321 (Excel Screenshot below)

So, P(X² < 18.56) = 1 - 0.9321

P(X² < 18.56) = 0.0679

The probability that the researcher obtains a sample variance less than 6400 if he/she draw random samples of size n = 30 is 0.0679