Question

A poll of university students in Canada found that one-quarter of all students completing an undergraduate program have 2 or more credit cards.
A random sample of n=431n=431 university students who recently completed an undergraduate program found that 100 had 2 or more credit cards. Does this sample support the one-quarter parameter?

a) Choose the null and alternative hypotheses
A. H0:p=0.25,HA:p>0.25
B. H0:pˆ=0.25,HA:pˆ≠0.25
C. H0:p=0.25 HA:p≠0.25
D. H0:pˆ=0.25,HA:pˆ<0.25
E. H0:p=0.25,HA:p<0.25H0

(b) Determine the absolute value absolute value of the test statistic for this test, to at least two decimal places.
Test Statistic =

（C）Determine the P-value for this test. Use at least three decimal places.
P=

(d) Based on the above calculations, we should reject/not reject the null hypothesis. Use alpha = 0.05

Answer 1

Solution :

a ) This is the two tailed test .

The null and alternative hypothesis is

H₀ : p = 0.25

H_a : p 0.25

n = 431

x = 100

= x / n = 100 / 431 = 0.23

P₀ = 0.25

1 - P₀ = 1 - 0.25 = 0.75

b ) Test statistic = z

= - P₀ / [P_{0 *} (1 - P₀ ) / n]

= 0.23 - 0.25/ [0.25 * 0.75 / 431 ]

= −0.862

Test statistic = z = −0.86

c ) P(z >−0.86 ) = 1 - P(z <−0.86 ) = 1 -0.8051

P-value = 2 * 0.1949 = 0.390

d ) = 0.05

P-value ≥

0.390 ≥ 0.05

Do not reject the null hypothesis .

There is insufficient evidence to suggest that