SOLUTION: 3. A marketing research analyst is interested in examining the statement made by the makers that cigarettes of brand Sea Breeze contain less than 3 milligrams of tar. The analyst

Algebra ->  Test -> SOLUTION: 3. A marketing research analyst is interested in examining the statement made by the makers that cigarettes of brand Sea Breeze contain less than 3 milligrams of tar. The analyst       Log On


   

Question 884111: 3. A marketing research analyst is interested in examining the statement made by the makers that cigarettes of brand Sea Breeze contain less than 3 milligrams of tar. The analyst randomly selected 60 cigarettes and found the mean amount of tar to be 2.7 milligrams. The population standard deviation is known to be 1.5 milligrams. Do the data support the claim? Test the appropriate hypotheses at 0.05 significance level.
Answer by Theo(13342) About Me  (Show Source):
You can put this solution on YOUR website!
null hypothesis is that mean >= 3 mg tar.

sample mean is 2.7 mg.
population standard deviation is 1.5.
sample size is 60
standard error is equal to population standard deviation divided by the square root of the sample size which is equal to 1.5 / sqrt(60) which is equal to .1936491673

null hypothesis is that the mean is greater than or equal to 3 mg.

alternate hypothesis is that the mean is less than 3 mg.

the critical alpha is .05.

this is a one sided alpha on the left side of the distribution curve only since the alternate hypothesis states less than rather than not equal to.

the z factor for a sample mean of 2.7 is equal to (sample mean minus population mean) divided by standard error which is equal to (2.7 - 3.0) / .1936491673.

this gets you a z factor of -1.549193339 which can be rounded to -1.55 which will favor the alternate hypothesis by a very small margin.

a z factor of -1.55 gets you an alpha of .0606

.0606 is greater than the critical alpha of .05 so the results are not considered to be statistically significant.

the null hypotheses that the mean value of tar is greater than or equal to 3 mg cannot be rejected because the results are within the 95% confidence limits agreed on before the study was conducted.

the z score table that was used can be found at:

http://lilt.ilstu.edu/dasacke/eco148/ztable.htm

this table gives you the area of the distribution curve that is to the left of the indicated z score.

with a negative z score, that area becomes your alpha.