Question

A recent study claimed that at least 15% of junior high students are overweight. In a sample of 160 students, 18 were found to be overweight. Test the claim, using α = 0.05.

1. State the null and alternative hypotheses for the test. [3 marks]

(b) Calculate the value of the test statistic for this test. [2 marks]

(c) Calculate the p-value for this test. [2 marks]

(d) State the conclusion of this test. Give a reason for your answer

Answer 1

given data are:-

hypothesized proportion () = 0.15

sample size (n) = 160

x = =number of overweight students = 18

level of significance () = 0.05

hypothesis:-

our null hypothesis contains the claim that is to be tested, i.e, at least 15 % students are overweight.

b). the test statistic be:-

c). the p value be = 0.092

[ from STANDARD NORMAL DISTRIBUTION: Table Values Represent AREA to the LEFT of the Z score, for z= -1.33]

d). conclusion:-

p value = 0.092 < 0.05 (alpha)

so, we do not have enough evidence to reject our null hypothesis.

hence, we conclude that,

There is not sufficient evidence to reject the claim at 0.05 level of significance.

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