Question

1. A cereal company claims the mean sodium content in one serving of its cereal is 230 milligrams. You work for a national health service and are asked to test this claim. You find that a random sample of 50 servings has a mean sodium content of 234 milligrams and a standard deviation of 10 mg. At α = 0.01, do you have enough evidence to reject the company’s claim?

Hypothesis:

Test statistic:

p-value:

Conclusion:

Interpretation:

Answer 1

Solution :

= 230

=234

S =10

n = 50

This is the two tailed test .

The null and alternative hypothesis is ,

H0 :    = 230

Ha :     230

Test statistic = t

= ( - ) / S / n

= (234-230) / 10 / 50

= 2.828

Test statistic = t = 2.828

P-value =0.0068

= 0.01  

P-value <

0.0068 < 0.01

Reject the null hypothesis .

There is sufficient evidence to claim that the population mean μ is different than 230, at the 0.01 significance level