Question

Assume that a simple random sample has been selected from a normally distributed population and test the given claim. Identify the null and alternative hypotheses, test statistic, P-value, and state the final conclusion that addresses the original claim. A simple random sample of 25 filtered 100 mm cigarettes is obtained, and the tar content of each cigarette is measured. The sample has a mean of 20.2 mg and a standard deviation of 3.36 mg. Use a 0.05 significance level to test the claim that the mean tar content of filtered 100 mm cigarettes is less than 21.1 mg, which is the mean for unfiltered king size cigarettes. What do the results suggest, if anything, about the effectiveness of the filters? What are the hypotheses? A. Upper H 0 : mugreater than21.1 mg Upper H 1 : muless than21.1 mg B. Upper H 0 : muequals21.1 mg Upper H 1 : mugreater than or equals21.1 mg C. Upper H 0 : muless than21.1 mg Upper H 1 : mugreater than or equals21.1 mg D. Upper H 0 : muequals21.1 mg Upper H 1 : muless than21.1 mg Your answer is correct. Identify the test statistic. tequals 0.9340193-1.339 negative 1.339 (Round to three decimal places as needed.) Identify the P-value. The P-value is 0.1931 nothing. (Round to four decimal places as needed.)

I need help with finding the p-value

Answer 1

Here, we are testing whether the mean tar content of filtered 100 mm cigarettes is less than 21.1 mg, therefore the null and the alternate hypothesis here would be given as:

Now the test statistic using the sample characterisitics are computed here as:

Therefore the test statistic value here is -1.339

Now as this is a one tailed for n-1 = 24 degrees of freedom, we get the p-value from the t distribution tables as:

p = P( t₂₄ < -1.339 ) = 0.0965

Therefore 0.0965 is the required p-value here.