Question

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

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