Respuesta :
Answer:
No, we will not reject the article’s claim.
Step-by-step explanation:
Here we are given that there is an article that claims only 30% of graduating seniors will buy a class ring and we have to test this claim.
Let P = claim that only 30% of graduating seniors will buy a class ring
Null Hypothesis, [tex]H_0[/tex] : P = 0.3
Alternate Hypothesis, [tex]H_1[/tex] : P [tex]\neq[/tex] 0.3
To test the above claim 15 randomly seniors are selected from the school and it is found that 4 are planning to buy a class ring.
Let X = Number of seniors planning to buy a class ring = 4
and n = Number of seniors selected from the school = 15
The test statistics we will be using is;
[tex]\frac{\frac{X\pm 0.5}{n}-P}{\sqrt{\frac{P(1-P)}{n}}}[/tex] follows N(0,1) {Here 0.5 is used for continuity correction}
Here we will add 0.5 to X because [tex]\frac{X}{n}[/tex] < P.
So, Test statistics = [tex]\frac{\frac{4+ 0.5}{15}-0.3}{\sqrt{\frac{0.3(1-0.3)}{15}}}[/tex] = 0
Now, since we are not given any level of significance so we assume it to be 5%. At 5% significance level critical values of z are -1.96 and 1.96 from the table{two-tail}. Since our test statistics lies between these two values so we have sufficient evidence to accept null hypothesis and conclude that claim of only 30% of graduating seniors will buy a class ring is correct.
Therefore, we will not reject the article’s claim.
