A study of the population of NUIG students showed that out of a sample of 155 students surveyed, 45 said they regularly cooked their own food during term time.Carry out a hypothesis test to determine if this gives evidence that more than 25% of the population of NUIG students regularly cooked their own food during term time, i.e test the hypotheses for true population proportion, H0: p= 0.25 versus Ha: p &gt; 0.25, at significance level α = 0.05Complete the test by filling in the blanks in the following:An estimate of the population proportion is .The standard error is . (3 dec places)The distribution is (examples: normal / t12 / chisquare4 / F5,6).The test statistic has value TS=. (2 dec places)Testing at significance level α = 0.05, the rejection region is: greater than (2 dec places).There (is / is no) evidence to suggest that the true proportion of the population of all NUIG students who regularly cooked their own food during term time, p, is greater than 0.25.

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A study of the population of NUIG students showed that out of a sample of 155 students surveyed, 45 said they regularly cooked their own food during term time.Carry out a hypothesis test to determine if this gives evidence that more than 25% of the population of NUIG students regularly cooked their own food during term time, i.e test the hypotheses for true population proportion, H0: p= 0.25 versus Ha: p &amp;gt; 0.25, at significance level α = 0.05Complete the test by filling in the blanks in the following:An estimate of the population proportion is .The standard error is . (3 dec places)The distribution is  (examples: normal / t12 / chisquare4 / F5,6).The test statistic has value TS=. (2 dec places)Testing at significance level α = 0.05, the rejection region is: greater than  (2 dec places).There  (is / is no) evidence to suggest that the true proportion of the population of all NUIG students who regularly cooked their own food during term time, p, is greater than 0.25.

Theresa Bullock · Accepted Answer

Given that, sample size n= 155And X= 45&amp;nbsp;Population proportion is given by,P= X/n= 45/155P= 0.290(b)We know that Q= 1-PQ= 1-0.290Q= 0.710Standard error for proportion is given by,SE. =&amp;nbsp;(PQ/n)=&amp;nbsp;0.290*0.710/155SE= 0.036(c) To test significance of proportion, we use z test (Normal Distribution) at the given level of significance.&amp;nbsp;(d) Test Statistic for proportion is,for test of significance for proportionz0&amp;nbsp;=&amp;nbsp;ρ−PPQnZ0→z&amp;nbsp;statisticρ→&amp;nbsp;same proportionP&amp;nbsp;→&amp;nbsp;population proportionQ&amp;nbsp;→&amp;nbsp;Q=(1-P)n&amp;nbsp;→&amp;nbsp;number of elements in large sampleGiven, sample proportion p= 0.25Z= (0.25-0.290)/0.036= 0.04/0.036= 1.11Testing at significance level alpha= 0.05 , the rejection region 1.645 is greater than 1.11&amp;nbsp;So we fail to reject null hypothesis.We conclude that There is no evidence to suggest that the true proportion of the population of all NUIG students who regularly cooked their own food during term time, p, is greater than 0.25.

A study of the population of NUIG students

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