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Answer:
For this case we can find the critical value with the significance level and if we find in the right tail of the z distribution we got:
The statistic is given by:
(1)
Replacing we got:
Since the calculated value is higher than the critical value we have enough evidence to reject the null hypothesis and we can conclude that the true proportion of households with one person is significantly higher than 0.27
Step-by-step explanation:
We have the following dataset given:
represent the households consisted of one person
represent the sample size
estimated proportion of households consisted of one person
We want to test the following hypothesis:
Null hypothesis:
Alternative hypothesis:
And for this case we can find the critical value with the significance level and if we find in the right tail of the z distribution we got:
The statistic is given by:
(1)
Replacing we got:
Since the calculated value is higher than the critical value we have enough evidence to reject the null hypothesis and we can conclude that the true proportion of households with one person is significantly higher than 0.27