Question

A nutrition lab 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 322.3 mg with a standard deviation of 17 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? a) Write appropriate hypotheses. Ho: u = 325 Ha: u < 325 The test statistic is t= - 1.00 . (Round to two decimal places as needed.) The P-value is 0.161. (Round to three decimal places as needed.) State your conclusion. Use a = 0.05. Do not reject the null hypothesis. There is not sufficient evidence to conclude that the mean sodium content is less than the value specified in the regulation.

Answer 1

Solution :

This is one tailed test .

The null and alternative hypothesis is ,

H₀ :  $\mu$ = 325

H_a : $\mu$ < 325

Test statistic(t) =

= ($\bar x$ - $\mu$) / s / $\sqrt$n

= (322.3 - 325) /17 / $\sqrt$40

Test statistic = -1.00

P(z < -1.00) = 0.159

P-value = 0.159

$\alpha$ = 0.05

P-value > $\alpha$

Do not reject the null hypothesis. There is not sufficient evidence to conclude that the mean sodium content is less than the value specified in the regulation.