Question

A university provides an opportunity for members to take part in training about how to respond to students’ questions. University managers believes that less than 60% of the members took part in the training. You are asked to examine whether there is any evidence to support this claim. You have surveyed 25 members and found that 17 of them have been benefited from the training.

Write down the null and alternative hypotheses in words.

Null hypothesis:
Alterative hypothesis:

State the direction of the test you are conducting and explain why you have chosen this test.

Using a level of significance (α) of 1%, determine the critical value(s).

Determine your decision rule (drawing a diagram on a paper may be helpful).

Calculate your test statistic.

Answer 1

Claim: To test whether that less than 60% of the members took part in the training about how to respond the students questions.

Hypothesis : Null and alternative hypothesis are

Ho: proportion of the members who took part in the training about how to respond the students questions are greater than equal to 60%

H1: proportion of the members who took part in the training about how to respond the students questions are less than 60%

i.e. Symbolically

v/s

Left tailed test(One tailed test)

Let x = Number of members who are benefited from the training =17

Given that

n= Total number of members =25

Therefore sample proportion is

By using One sample proportion test we can test this hypothesis

Assumptions of One sample proportion test are :

1) The data are simple random values from the population

2) Here n*p = 25 * 0.60 = 15 and n * q = 25*(1-0.60) = 10

Here both n*p and n*q are greater than or equal to 10

Therefore One sample proportion test is approporiate to use

Test statistics:

we get Test statistics = z = 0.816

Critical value :

Based on the information provided, the significance level is α=0.01, and the critical value for a left-tailed test is

..................(By using Standard normal table)

Decision Rule: Since it is observed that   then it is then concluded that the null hypothesis is not rejected.

Graphically