A manufacturer of candy must monitor the temperature at whic

A manufacturer of candy must monitor the temperature at which the candies are baked. Too much variation will cause inconsistency in the taste of the candy. Past records show that the standard deviation of the temperature has been 1.2 degrees F. A random sample of 30 batches of candy is selected, and the sample deviation of the temp is 0.89 degreed F. Test the claim that the population standard deviation is less than 1.2 degrees F. Use a 0.01 significance level and the p-value method. Show work.
A) Null hypothesis: ?
B) Alternative hypothesis: ?
C) test statistic: ?
D) p-value: ?
E) initial conclusion: ?
F) conlsuion: ?

Solution

A & B)
Here the hypotheses of interest are,
H_0:^2<=1.2^2 and H_a:^2>1.2^2

C)
Test statistics = (n-1)S^2/(^2 )=((30-1)*(0.89)^2)/(1.2)^2 =15.9520

D)
^2 p_value = Chi2=15.9520, DF=29   
The two-tailed P value equals 0.9761          
  
E)
standard deviation has increased above 1.2 degrees

F)
As the p-value is larger than the significance level so we are Failed to Rejecting the null hypothesis and concluding that there is no significant evidence that the population standard deviation has increased above 1.2 degrees Fahrenheit.