Question

I pulled out an old 1000-piece puzzle yesterday to complete, but I’m not sure if it is missing any pieces. I know from completing it before, there are 126 edge pieces. I randomly pull out 100 pieces and find 10 edge pieces. Conduct a one-sample hypothesis test to determine whether, using a 1% confidence level, the true proportion of edge pieces is less than the population proportion (i.e. that I am missing pieces). Make sure to give your conclusion as a complete sentence and in context.  

Answer 1

Solution :

This is the left tailed test .

The null and alternative hypothesis is

H0 : p = 0.50

Ha : p < 0.50

= x / n = 10 /100 = 0.10

P0 = 0.50

1 - P0 = 0.50

Test statistic = z

= - P0 / [P0 * (1 - P0 ) / n]

=0.10 -0.50 / [0.50*(0.50) /100 ]

= -8

P(z < -8) = 0

P-value = 0.0000

= 0.01

0 < 0.01

Reject the null hypothesis .

There is sufficient evidence to suggest that