Sodium in Breakfast Cereal. Use the following information for Exercises 78–83. A random sample of 23 breakfast cereals containing sodium had a mean sodium content per serving of 192.39 grams. Assume that the population standard deviation equals 50 grams. We are interested in whether the population mean sodium content per serving is less than 210 grams.

Question 9.187

81. Use the equivalence between two-tailed hypothesis tests and confidence intervals to perform a set of hypothesis tests, as follows.

  1. Construct a 95% Z confidence interval for the population mean sodium content. (Hint: See Section 8.1.)
  2. Use the confidence interval to test, at level of significance , whether the population mean sodium content differs from the following amounts:
    1. 200
    2. 215
    3. 170
    4. 160

9.3.81

(a) (171.96, 212.82)

(b)

Value of
 Form of hypothesis test,
with 		Where lies
in relation to
95% confidence
interval		 Conclusion of
hypothesis test
(i) 200 Inside Do not reject
(ii) 215 Outside Reject
(iii) 170 Outside Reject
(iv) 160 Outside Reject