A nutrition laboratory tests 40 "reduced sodium" hotdogs, finding that the mean sodium content is 309 mg, with a standard deviation of 35 mg.

a) Find a 95% confidence interval for the mean sodium content of this brand of hot dog.

b) What assumptions have you made in thisinference? Are the appropriate conditionssatisfied?

c) Explain clearly what your interval means.

a) Find a 95% confidence interval for the mean sodium content of this brand of hot dog.

,

(Round to one decimal place asneeded.)

b) What assumptions have you made in thisinference?

A.

We have assumed that the hot dog weights are random and that the distribution of the population of hot dog weights is not biased.

B.

We have assumed that the hot dog weights are independent and that the distribution of the population of hot dog weights is normal.

C.

We have assumed that the hot dog weights are not multimodal and that the distribution of the population of hot dog weights does not contain any outliers.

Is the randomization conditionsatisfied?

A.

No, there is evidence to believe that the hot dogs were not sampled at random.

B.

Yes, there is definitely evidence to believe that the hot dogs were sampled at random.

C.

No, because the hot dogs came from the same package.

D. Wedon't know that the hot dogs were sampled atrandom, but it is reasonable to think that they were.

Is the10% conditionsatisfied?

A.

No, 40 hot dogs are less than10% of all hot dogs.

B.

No, 40 hot dogs are more than10% of all hot dogs.

C.

Yes, 40 hot dogs are more than10% of all hot dogs.

D.

Yes, 40 hot dogs are less than10% of all hot dogs.

Is the nearly normal conditionsatisfied?

A.

Yes, the sample of 40 hot dogs came from a distribution that is approximately normal.

B.

No, the sample of 40 hot dogs did not come from a distribution that is approximately normal.

C.

Wedon't know, but since the sample of 40 hot dogs is 40 ormore, it is okay to proceed.

c) Explain clearly what your interval means.

A.

95% of all"reduced sodium" hot dogs will have a mean sodium content that falls within the interval.

B.

We are 95% confident that the interval contains the true mean sodium content in this type of"reduced sodium" hot dogs.

C.

The interval contains the true mean sodium content in this type of"reduced sodium" hot dogs 95% of the time.

D.

95% of the sodium content in this type of"reduced sodium" hot dog will be contained in the interval.