Question

The price of a gallon of milk at 16 randomly selected Arizona stores is given below. Assume that milk prices are normally distributed. At the α=0.10α=0.10 level of significance, is there enough evidence to conclude that the mean price of a gallon of milk in Arizona is less than $3.00? (Round your results to three decimal places)

Which would be correct hypotheses for this test?

• H0:μ=$3H0:μ=$3, H1:μ≠$3H1:μ≠$3
• H0:μ=$3H0:μ=$3, H1:μ>$3H1:μ>$3
• H0:μ≠$3H0:μ≠$3, H1:μ=$3H1:μ=$3
• H0:μ<$3H0:μ<$3, H1:μ=$3H1:μ=$3
• H0:μ=$3H0:μ=$3, H1:μ<$3H1:μ<$3

Gallon of Milk prices:

2.85	3.23	3.23	2.93
3.07	2.75	3.17	2.51
2.89	3.23	2.79	2.77
2.61	3.17	2.85	2.75

test statistic:



Give the P-value:

Answer 1

H0:μ=$3, H1:μ<$3

We have for given sample,              
Population mean for given sample=$3
Sample mean=$2.925      
Sample standard deviation s=$0.232  
Sample size =n=   16      
              
Degree of freedom = n-1 =15  
              
              
              
t test statistic formula is              


=-1.293          

P value is =0.108........................by using Excel command TDIST(-1.293,15,1)

P value is =0.108 > 0.10

Therefore, we fail to reject H0 at

We do not have sufficient evidence at to say that, the mean price of a gallon of milk in Arizona is less than $3.00