Probability Question

[roby]

Hi can you help me with this problem please. a bank claimed 40% of its customers use internet banking. in random checks they found 170 of the 500 customers used internet banking in a day. does the sample result mean the bank's claim is too large. perform an hypothesis test and calculate the P-value.
thank you for your previous help
roby

[JohnM]

This is a directional hypothesis test. The bank claims P = 0.40, but the sample data = 170/500 = 0.34.

Ho: P = 0.40
Ha: P < 0.40

Z = (p - P) / Sp

where
"small" p = 0.34
"big" P = 0.40
Sp = sqrt(P*q/n) --> q = 1 - P = 0.6, n = 500

Once you find Z, determine its probability in the normal distribution tables (this is the p-value).

If it's really small (say < .05), you have enough evidence to reject the bank's claim.