Question

At a certain college, it is estimated that at most 25% of the students ride bicycles to class. Does this seem to be a valid estimate if, in a random sample of 90 college students, 28 are found to ride bicycles to class? Use a 0.05 level of significance.

Answer 1

Answer: No, it does not seem to be a valid estimate if in a random sample of 90 college students, 28 are found to ride bicycles to class.

Step-by-step explanation:

Since we have given that

Number of college students = 90 = n

Number of students ride bicycles to class = 28 = x

So, $\hat{p}=\dfrac{x}{n}=\dfrac{28}{90}=0.31$

Hypothesis :

$H_0:p=\hat{p}\\\\H_a:\hat{p}\leq p$

So, the test statistic value would be

$\dfrac{\hat{p}-p}{\sqrt{\dfrac{p(1-p)}{n}}}\\\\z=\dfrac{0.31-0.25}{\sqrt{\dfrac{0.25\times 0.75}{90}}}\\\\z=\dfrac{0.06}{0.0456}\\\\z=1.136$

At 0.05 level of significance,

critical value z = 1.96

Since 1.96>1.136

So, we will accept the null hypothesis.

Hence, No, it does not seem to be a valid estimate if in a random sample of 90 college students, 28 are found to ride bicycles to class.