Question

The average cost of braces in the US is μ = 5600 with σ = 580 dollars. A dentist worries he is charging more that the national average. A random sample of 50 patients found a mean of $5800. Is there enough evidence to say this dentist is charging more than the national average? (Use α = .01 .

Answer 1

Solution :

This is the right tailed test,  

The null and alternative hypothesis is ,

H₀ :   = 5600

H_a : > 5600

Test statistic = z =

= ( - ) / / n

= (5800 - 5600) / 580 / 50

Test statistic = z = 2.44

P(Z > 2.44) = 1-P (Z < 2.44) = 1 - 0.9927

P-value = 0.0073

= 0.01

P-value <

Reject the null hypothesis .

There is sufficient evidence to suggest that  say this dentist is charging more than the national average