Question

pH is a measure of acidity that winemakers must watch. A "healthy wine" should have a pH in the range 3.1 to 3.7. The target standard deviation is σ = 0.10 (i.e., σ2 = 0.01). The pH measurements for a sample of 16 bottles of wine are shown below. At α = .05 in a two-tailed test, is the sample variance either too high or too low?                        
3.49   3.54   3.58   3.57   3.54   3.34   3.48   3.60
3.48   3.27   3.46   3.32   3.51   3.43   3.56   3.39

(a)   Choose the correct null and alternative hypotheses.
      
a.   H0: σ2 = 0.01 vs. H1: σ2 ≠ 0.01
b.   H0: σ2 ≤ 0.01 vs. H1: σ2 > 0.01
c.   H0: σ2 ≥ 0.01 vs. H1: σ2 < 0.01
   
   a
   b
   c

(b)   Choose the correct decision rule.
      
a.   Reject the null hypothesis if χ2 > 25.00 or χ2 < 7.261
b.   Reject the null hypothesis if χ2 < 27.49 or χ2 > 6.262
c.   Reject the null hypothesis if χ2 > 27.49 or χ2 < 6.262
   
   a
   b
   c

(c)   Calculate χ2. (Round your answer to 2 decimal places.)
χ2     
  
(d)   Choose the correct conclusion.
      
a.   Fail to reject H0. There is not enough evidence to conclude that the variance is different from .01.
b.   Reject H0. There is significant evidence to conclude that the variance is different from .01.
      

   a
   b

Answer 1

Sr.No.	xi	(xi-xbar)2
1	3.49	0.000306
2	3.54	0.004556
3	3.58	0.011556
4	3.57	0.009506
5	3.54	0.004556
6	3.34	0.017556
7	3.48	5.62E-05
8	3.6	0.016256
9	3.48	5.62E-05
10	3.27	0.041006
11	3.46	0.000156
12	3.32	0.023256
13	3.51	0.001406
14	3.43	0.001806
15	3.56	0.007656
16	3.39	0.006806
Total	55.56	0.1465