SOLUTION: a harris poll found that 35% of people said that they drink a caffeinated beverage to combat mid day drowsiness. A recent survey found that 19 of 48 people stated that they drank a

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Question 1207365: a harris poll found that 35% of people said that they drink a caffeinated beverage to combat mid day drowsiness. A recent survey found that 19 of 48 people stated that they drank a caffeinated beverage to combat midday drowsiness. At Alpha=0.05 is the claim of the percentage found in the harris poll believable?
Answer by Theo(13342) About Me  (Show Source):
You can put this solution on YOUR website!
population mean assumed to be .35
sample size = 48
sample mean is 19/48 = .3958 rounded to 4 decimal places.

standard error for the test assumed to be sqrt(.35 * .65 / 48) = .0688 rounded to 4 places.

z = (x - m) / s
z is the z-score.
x is the sample mean.
m is the population mean.
s is the standard error.

formula becomes z = (.3958 - .35) / .0688 = .6657 rounded to 4 decimal places.

two tail critical z-score at .05 alpha is plus or minus 1.96.

z-score of .6657 is well within the critical z-score limits.
conclusion is that the results are not significant enough to refute the claim that the proportion is .35.
alternate hypothesis is rejected in favor of the null hypothesis.

null hypothesis is that the ratio is .35
alternate hypothesis is that it is different than .35.

here's a reference.

https://sixsigmastudyguide.com/one-and-two-sample-proportion-hypothesis-tests/#:~:text=The%20One%20Sample%20Proportion%20Test,called%20the%20hypothesis%20of%20inequality.