Question

Asked Nov 20, 2019

The nutrition lab in Chapter 17, Exercise 38 tested 40 hot dogs to see if their mean sodium content was less than the 325-mg upper limit set by regulations for “reduced sodium” franks. The mean sodium content for the sample was 322.0 mg with a standard deviation of 18 mg. Assume that the assumptions and conditions for the test are met.

a) Test the hypothesis that the mean sodium content meets the regulation.

b) Will a larger sample size ensure that the regulations are met?

Step 1

a.

From the provided information, the sample size of hot dogs (*n*) = 40

Let *µ* represents the population mean. The sample size (*x̄*) = 322.0 mg and sample standard deviation (*s*) = 18 mg

The hypothesis can be constructed as:

Null hypothesis, *H*_{0}:* µ*=325 mg (The mean sodium content is equal to the upper limit set by regulations for “reduced sodium” franks.)

Alternative hypothesis, *H*_{a}:* µ*<325 mg (The mean sodium content is less than the upper limit set by regulations for “reduced sodium” franks.)

Step 2

The degree of freedom = (*n*-1)

= 40-1

= 39

The level of significance is not provided so it can be taken as 0.05.

The *t*-critical values at 0.05 level of significance with 39 degree of freedom from the *t*-value table is -1.6849.

Step 3

The test statistic value ca...

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