According to data, a particular brand of cigarettes contain an average of 1.4 mi

Question

According to data, a particular brand of cigarettes contain an average of 1.4 milligrams of nicotine. An advocacy group commissions an independent test to see if the mean nicotine content is higher than the industry laboratory claims.

(a) What are H0 and Ha?

H0: > 1.4 mg;   Ha: = 1.4 mg

H0: = 0.0 mg;   Ha: > 0.0 mg

H0: = 1.4 mg;   Ha: > 1.4 mg

H0: < 0.0 mg;   Ha: = 0.0 mg

H0: = 1.4 mg;   Ha: 1.4 mg

(b) Suppose that the test statistic is z = 2.34. Is this result significant at the 5% level?

Yes, because z > 1.645 and P < 0.05.Yes, because z < 1.645 and P < 0.05.    No, because z > 1.645 and P > 0.05.Yes, because z > 1.645 and P > 0.05.No, because z < 1.645 and P > 0.05.

(c) Is the result significant at the 1% level?

Yes, because z < 2.326 and P < 0.01.No, because z > 2.326 and P > 0.01.    No, because z > 2.326 and P > 0.01.No, because z < 2.326 and P > 0.01.Yes, because z > 2.326 and P < 0.01.

Explanation / Answer

a) Here the claim is to check whether mean nicotine content is higher than the industry laboratory i.e. 1.4 milligrams. So,

Null and alternative hypotheses will be:

H0: = 1.4 mg;   Ha: > 1.4 mg

Option C is correct.

For a right tailed test,

p - value corresponding to z statistic of 2.34 is:

P(z > 2.34) = 0.0096

Hence,

b) The result would be significant at 5% level because z > 1.645 and P < 0.05. Option 1st is correct.

c) The result would be significant at 1% level because z > 2.326 and P < 0.01. Option 4th is correct.

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