- Past records show that \(15 \%\) of customers at a shop buy chocolate. The shopkeeper believes that moving the chocolate closer to the till will increase the proportion of customers buying chocolate.
After moving the chocolate closer to the till, a random sample of 30 customers is taken and 8 of them are found to have bought chocolate.
Julie carries out a hypothesis test, at the 5\% level of significance, to test the shopkeeper's belief.
Julie's hypothesis test is shown below.
\(\mathrm { H } _ { 0 } : p = 0.15\)
\(\mathrm { H } _ { 1 } : p \geqslant 0.15\)
Let \(X =\) the number of customers who buy chocolate.
\(X \sim \mathrm {~B} ( 30,0.15 )\)
\(\mathrm { P } ( X = 8 ) = 0.0420\)
\(0.0420 < 0.05\) so reject \(\mathrm { H } _ { 0 }\)
There is sufficient evidence to suggest that the proportion of customers buying chocolate has increased.
- Identify the first two errors that Julie has made in her hypothesis test.
- Explain whether or not these errors will affect the conclusion of her hypothesis test. Give a reason for your answer.
- Find, using a 5\% level of significance, the critical region for a one-tailed test of the shopkeeper's belief. The probability in the tail should be less than 0.05
- Find the actual level of significance of this test.