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?

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?

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Expert Answer

Step 1

a.

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

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

The hypothesis can be constructed as:

Null hypothesis, H0: µ=325 mg (The mean sodium content is equal to the upper limit set by regulations for “reduced sodium” franks.)

Alternative hypothesis, Ha: 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...

t =
322-325
18
40
=-1.054
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t = 322-325 18 40 =-1.054

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