Question

The probability that a rose bud blooms is p. In a random sample of 500 rose buds, 240 of them
bloomed.
With the data obtained in a random sample, a hypothesis test at the 1% level of significance is
carried out to determine whether p is different from 0.45.
a) State the null and alternative hypothesis [2]
b) Calculate the test Statistics [2]
c) What is the p-value of the test? [2]
d) Supporting your answer, state the conclusion of the test

Answer 1

$m=500, x = 240$

$P = x/m =240/500=0.48$

$q = 0.52, \alpha = 1\%$ , $P_{0} = 0.45$

a) null hypothesis, $P= P_{0} = 0.45$

alternative hypothesis, $P = P_{0} = 0.45$

b) $Z = (P-P_{0}) \div \sqrt{Pq/m} = (0.48-0.45) \div \sqrt{\frac{0.48\times 0.52}{500}} = 0.03/0.22=1.36$

$|Z| = 1.36 (test$ $statistics)$

c) $P-value = 2\times P [Z\text{\textgreater}1.36]=2\times [0.5-P|0\text{\textless Z \text{\textless}1.36|}]$

$=2\times (0.5-0.4131) = 0.1738$

d) $P - value \text{\textgreater} \alpha,$ so we can not reject our new hypothesis, meaning the are both the same.