A researcher is testing a theory that the diameters of certa

A researcher is testing a theory that the diameters of certaion subatomic particles are not meaningfully different. This being the case, the researcher believes that the variance shuold be no more than 1. Do the hypothesis test to the claim of the researcher. For a random sample of 27 measurements the average lenght was 23.4 nanometers with a standard deviation of 2.4 nanometers. Assume the diameters for this subatomic particle is normally distributed.

a. Give the null and research hypothesis

H₀:

H₁:

b. The test statistic is _______________ = ___________________

c. The P-value is ________________________

d. Interpret the results so that someone unfamiliar with statistics would understand.

Solution

(a) Let o^2 be the variance

Ho: o^2 =1

Ha: o^2 >1

----------------------------------------------------------------------------------------------

(b) The test statistic is

Chisquare= (n-1)*s^2/o^2

=(27-1)*2.4^2/1

=149.76

----------------------------------------------------------------------------------------------

(c) The degree of freedom =n-1=27-1=26

So The P-value is P(X^2 with df=26 >149.76) =0 (from chisquare table)

----------------------------------------------------------------------------------------------

(d) Based on the statisitcal analsysis, we can not conclude that the variance shuold be no more than 1