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

H_{0} : p = 0.25

H_{a} : p
0.25

n = 431

x = 100

= x / n = 100 / 431 = 0.23

P_{0} = 0.25

1 - P_{0} = 1 - 0.25 = 0.75

b ) Test statistic = z

=
- P_{0} / [P_{0
*} (1 - P_{0} ) / 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

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