Question

The business college computing center wants to determine the proportion of business students who have personal computers (PC's) at home. If the proportion exceeds 35%, then the lab will scale back a proposed enlargement of its facilities. Suppose 300 business students were randomly sampled and 122 have PC's at home. Should the college scale back on the proposed enlargement of its facilities? Use alpha = .05.

a) Check the assumptions:

b) Hypotheses (State in symbols and in words): Ho:

Ha:

c) Test Statistic: d) Sketch:

e) P-Value:

f) Conclusion:

Answer 1

Given : n=300 , X=122 ; The estimate of the sample proportion is ,

a) The sample is stated to be a simple random sample , the values of is greater than 10 and the sample size can be assumed to be less than or equal to 5%of the population size.

b) Hypothesis: Vs   ( Claim )

The hypothesis is word :

Ho : The lab will not  scale back a proposed enlargement of its facilities

H1: The lab will scale back a proposed enlargement of its facilities

c) The test statistic is ,

d)

e) The p-value is ,

p-value= ; From standard normal distribution table

f) Decision : Here , p-value = 0.0167 < 0.05

Therefore , Reject the null hypothesis.

Conclusion : Hence , there is enough evidence to support the claim that the percentage exceeds 35%.

i.e. The lab will scale back a proposed enlargement of its facilities