Question

Perform hypothesis tests on the following five problems.

Assume that a simple random sample has been selected from a normally distributed population and test the given claim. Identify the hypotheses, test statistic, critical value(s), decision about the null hypothesis, and final conclusion.

1. 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 19.6 mg and a standard deviation of 3.21 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.

Answer 1

Solution :

= 21.1

=19.6

S =3.21

n = 25

This is the left tailed test .

The null and alternative hypothesis is ,

H0 :    = 21.1

Ha : < 21.1

Test statistic = t

= ( - ) / S / n

= (19.6 -21.1) / 3.21 / 25

= -2.336

Test statistic = t = -2.336

P-value =0.0141

= 0.05  

P-value <

0.0141 < 0.05

Reject the null hypothesis .

There is sufficient evidence to suggest that