Answer to Question #258470 in Statistics and Probability for klow

Question

1.                 A certain restaurant advertises that it puts 0.25 pound of beef in its burgers. A customer who frequents the restaurant thinks the burgers actually contain less than 0.25 pound of beef. With permission from the owner, the customer selected a random sample of 60 burgers and found the mean and standard deviation to be 0.22 and 0.77, respectively.

a.   Test the customer’s assertion at 0.01 level of significance using the critical value approach.

b.   Will you reject Ho in (a) at 0.01 level of significance?

 

Solution:

a.   Ho: ____________________                  Ha: _____________________

b.   𝛼 = _____________________ ;   critical value: ________________   ; type of test: ___________       c. Criterion region: _____________________________________________________________   d. Test Statistic: ___________________________

Answer 1

Solution:

a. Ho: $\mu=0.25$

Ha: $\mu<0.25$

$n= 60 \\ \bar{x} = 0.22 \\ s= 0.77$

Test-statistic

$t = \frac{\bar{x} - \mu}{s / \sqrt{n}} \\ t =\frac{0.22-0.25}{0.77 / \sqrt{60}} \\ t = \frac{-0.03}{0.0994} = -0.301 \\ df=n-1=59 \\ α=0.01$

One-tailed test

$t_{crit} = 2.391$

Reject the null hypothesis if $t ≤ -t_{crit}$

$t= -0.301 > t_{crit} = -2.391$

We accept the null hypothesis at 0.01 level of significance.

b. No, we will accept H₀.

We can conclude that the burgers actually contain 0.25 pounds of beef.