Question

More and more people are buying store brand products rather than national brand products. A coffee company claims that 40% of their customers buy national brand coffee. A random sample of 700 people who buy coffee showed that 259 of them buy national brand coffee. Use a 1% level of significance to test the percentage of people who buy national brand coffee is different from 40%

Answer 1

Solution :

This is the two tailed test .

The null and alternative hypothesis is

H0 : p = 0.40

Ha : p 0.40

n = 700

x = 259

= x / n = 259 / 700 =0.37

P0 = 0.40

1 - P0 = 1 - 0.40 =0.60

Test statistic = z

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

=0.37 -0.40/ [(0.40*0.60) / 700]

= -1.62

Test statistic = z = -1.62

P(z < -1.62 ) = 0.0526

P-value = 2 * 0.0526 = 0.1052

= 0.01

P-value <

0.1052 > 0.01

Fail to reject the null hypothesis .

There is insufficient evidence to suggest that