Question

Suppose you take a sample of 81 offenders from Maryland state prisons and you find that the average number of tattoos is 4.4 with a standard deviation of 1.9. According to Tattoo Me magazine, the average number of tattoos for all incarcerated offenders is 2.9. a) Test the null hypothesis that Maryland offenders have the same mean number of tattoos as other offenders in the general incarcerated population against the alternative that they have a significantly different mean number of tattoos. Use an alpha level of .05. Interpret your results.

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Answer 1

Solution :

This is the two tailed test .

The null and alternative hypothesis is ,

H₀ :   = 2.9

H_a :    2.9

Test statistic = z

= ( - ) / / n

= (4.4 - 2.9) / 1.9 / 81

= 7.11

P(z > 7.11) = 1 - P(z < 7.11) = 0

P-value = 0

= 0.05

P-value <

Reject the null hypothesis .

There is sufficient evidence to support that the they have a significantly different mean number of tattoos .