Question

Use the WSRT to answer the question below. Assume that the data are simple random samples from a systematic distribution.

A consumer groups claims that a particular brand of cigarette has a median nicotine content exceeding 2.00 mg. A random sample of ten cigarettes of this brand yielded the following nicotine contents:

2.06 2.14 1.82 2.21 2.36 2.03 1.93 1.72 2.15 2.07

Is there sufficient evidence to support the claim of the consumer group? ( α =.05)

Answer 1

To test the hypotheses at 0.05 level of significance we will use T test statistic here since sample size is less than 30 and sample standard deviation is given.

The hypotheses are

Rejection region:

Reject Ho if T calculated is greater than t(9.05,9) ,here 9 is degree of freedom calculated as n-1.

Test statistic:

Here

Calculated by excel as 2.049

And standard deviation also calculated using excel as s= 0.188

Now by test statistic formula

T=0.824

P value:

P value associated with T statistic and Degree of freedom California t table as

0.1<P value<0.25

Conclusion:

Since T calculated is less than t(0.05,9)=1.833, and P value >0.05 hence we fail to reject the null hypothesis, and conclude that we do not have enough evidence to support the claim.