Question

# Assume that a simple random sample has been selected from a normally distributed population and test...

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 18.8 mg and a standard deviation of 3.87 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?

we have to test whether the mean tar content of filtered 100 mm cigarettes is less than 21.1 ​mg or not. So, it is a left tailed hypothesis test

Given that

xbar(sample mean) = 18.8, s(sample standard deviation) = 3.87 and n = 25 (sample size)

mu = 21.1 (population mean)

test statistic =

degree of freedom =n-1

= 25-1

= 24

Using t distribution table with test statistic (-2.97), we get

p value = 0.0033

p value is less than 0.05 significance level, we can reject the null hypothesis

We can conclude that the mean is significantly less than 21.1mm

So, we can say that filters are effective in reducing the tar content

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