Geoff has been running a restaurant in the city for many years. He knows from experience that the proportion of customers that leave tips at this restaurant is 0.62. Geoff has recently opened a restaurant in a suburban area. It seems that tipping habits are different in the suburbs: Geoff believes that the proportion of customers that tip at his new restaurant () may be different to 0.62. He conducts a hypothesis test to find out.

The null and alternative hypotheses are:

H₀:= 0.62

H_A: 0.62

Geoff takes a random sample of 101 customers and notes whether or not they leave a tip. In this sample, the proportion of people that leave a tip is 0.67. You may find thisstandard normal tableuseful throughout this question.

a)Calculate the test statistic (z). Give your answer to 2 decimal places.

z =

b)Calculate the P-value. Give your answer as a decimal to 4 decimal places.

P =