Question

1. A random sample of 103 students and 65 said they exercise regularly. Is this enough to say that 75% of the students exercise regularly?
   1. State your null hypothesis and alternative hypothesis.
   2. Calculate the test statistic.
   3. Find the p-value.
   4. Is this enough to claim 75% of the students exercise regularly?

Answer 1

Solution :

Given that,

x = 65

n = 103

a. The null and alternative hypothesis is

H0 : p = 0.75

Ha : p 0.75

This is the two tailed test .

= x / n = 65 / 103 = 0.6311

P0 = 75% = 0.75

1 - P0 = 1 - 0.75 = 0.25

b. Test statistic = z

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

= 0.6311 - 0.75 / [0.75 * (0.25) / 103]

= −2.788

c. P-value = 0.0053

= 0.05    

0.0053 < 0.05

P-value <

Reject the null hypothesis .

d. There is sufficient evidence to test the claim.