In 2003 32 of university undergraduate students had at least

In 2003, 32% of university undergraduate students had at least one tattoo. A health practitioner obtains a random sample of 1077 university undergraduates and finds that 332 have at least one tattoo. Has the proportion of university undergraduate students with at least one tattoo changed since 2003 Use the alpha = 0.01 level of significance. Complete parts (a) through (d) below. Determine the null and alternative hypotheses. H_0 : H_1 : Calculate the P-value. P-value =

Solution

Test Statistic
No. Of Success chances Observed (x)=332
Number of objects in a sample provided(n)=1077
No. Of Success Rate ( P )= x/n = 0.3083
Success Probability ( Po )=0.32
Failure Probability ( Qo) = 0.68
we use Test Statistic (Z) for Single Proportion = P-Po/Sqrt(PoQo/n)
Zo=0.30826-0.32/(Sqrt(0.2176)/1077)
Zo =-0.8257
P-Value: Two Tailed ( double the one tail ) - Ha : ( P != -0.82568 ) = 0.409