Question

12. A manufacturer claims that the average tar content of a certain kind of cigarette is $$ \mu = 14.0 $$ In an attempt to show that it differs from this value, five random measurements were made of the tar content (mg per cigarette): 14.5 14.2 14.4 14.3 14.6 (a) Show the the difference between the mean of this sample and the average tar claimed by the manufacturer is statistically significant at $$ \alpha = 0.05 $$. Assume normality. (b) suppose that the first measurement is recorded incorrectly as 16.0 instead of 14.5. Show that even though the mean of the sample increases, the null hypothesis is not rejected at $$ \alpha = 0.05 $$. Explain the apparent paradox that even though the difference between observed $$ \bar{x} $$ and $$ \mu $$ has increased, the null hypothesis is no longer rejected.

Name: 12 a manufacturer claims that the average tar content of a certain kind of cigarette is mu 140 in an attempt to show that it differs from this value five random measurements were made of the 22871
Uploaded: 2022-08-12T17:50:40-08:00
Duration: 2 min 55 s
Channel: David Nguyen
Description: 12 a manufacturer claims that the average tar content of a certain kind of cigarette is mu 140 in an attempt to show that it differs from this value five random measurements were made of the 22871

          12. A manufacturer claims that the average tar content of a certain kind of cigarette is $$ \mu = 14.0 $$ In an attempt to show that it differs from this value, five random measurements were made of the tar content (mg per cigarette):

14.5 14.2 14.4 14.3 14.6

(a) Show the the difference between the mean of this sample and the average tar claimed by the manufacturer is statistically significant at $$ \alpha = 0.05 $$. Assume normality.

(b) suppose that the first measurement is recorded incorrectly as 16.0 instead of 14.5. Show that even though the mean of the sample increases, the null hypothesis is not rejected at $$ \alpha = 0.05 $$. Explain the apparent paradox that even though the difference between observed $$ \bar{x} $$ and $$ \mu $$ has increased, the null hypothesis is no longer rejected.

12 a manufacturer claims that the average tar content of a certain kind of cigarette is mu 140 in an attempt to show that it differs from this value five random measurements were made of the 22871

Added by Cristian V.

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