Question

Fry Appliances inc manufactures cast iron skillets. Their top selling skillet is designed to weigh 10 lbs. the quality control department randomly collects 41 skillets form the production line and weighs them. These 41 skillets had an average weight of 9.9 lbs with a standard deviation of 0.87 lbs. assume the wights of the skillets are normally distributed

Is it believable that the mean skillet weight is lighter than 10.0 lbs? conduct the appropriate hypothesis test using α=0.05

Answer 1

Solution :

Given that,

Population mean = = 10

Sample mean = = 9.9

Sample standard deviation = s = 0.87

Sample size = n = 41

Level of significance = = 0.05

Step 1 :

This is a left (One) tailed test,

The null and alternative hypothesis is,  

Ho: 10

Ha: 10

Step 2 :

The test statistics,

t =( - )/ (s /n)

= ( 9.9 - 10 ) / ( 0.87 / 41 )

= -0.736

Step 3 :

Critical value of  the significance level is α = 0.05, and the critical value for a left-tailed test is

= -1.684

Since it is observed that t = -0.736 > = -1.684 , it is then concluded that fail to reject the null hypothesis .

Step 4 :

P- Value = 0.2330   

The p-value is p =0.2330 > 0.05,it is then concluded that fail to reject the null hypothesis .

Step 5 :

Conclusion :

It is concluded that the null hypothesis Ho is fail to rejected. Therefore, there is not enough evidence to claim that the mean skillet weight is lighter than 10.0 lbs, at the 0.05 significance level.