Test the null hypothesis H0 : p = 0.5 against the alternative hypothesis HA : p < 0.5 , when 90 individuals in a random sample of 218 have a characteristic of interest.
a) Calculate the value of the z test statistic, for testing the null hypothesis that the population proportion is 0.5.
Round your response to at least 3 decimal places.
b) The p-value falls within which one of the following ranges:
p-value > 0.50
0.10 < p-value < 0.50
0.05 < p-value < 0.10
p-value < 0.05
c) What conclusion can be made, at the 5% level of significance?
There is sufficient evidence to reject the null hypothesis, in favour of the alternative that the population proportion is less than 0.5.
There is insufficient evidence to reject the null hypothesis, and therefore no significant evidence that the population proportion is not 0.5.