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 80 college students, 25 are found to ride bicycles to class? Use a 0.01 level of significance. Click here to view page 1 of the standard normal distribution table. Click here to view page 2 of the standard normal distribution table. Let a success be a student that rides a bicycle to class. Identify the null and alternative hypotheses. O A. Ho:p+0.25 H : p = 0.25 B. Ho: p < 0.25 Hy: p = 0.25 C. Ho:p=0.25 Hj: p<0.25 0 D. Ho: p = 0.25 Hy:p0.25 O E. Ho: p = 0.25 Hi:p>0.25 0 F. Ho:p> 0.25 Hy: p = 0.25 Identify the critical region. Select the correct choice below and fill in the answer box(es) to complete your choice. (Round to two decimal places as needed.) O A. z< or z> B. Z O C. Z> Find the test statistic. Z= (Round to two decimal places as needed.)

Answer 1

Solution :

This is the left tailed test .

The null and alternative hypothesis is

H₀ : p =0.25

H_a : p < 0.25

n = 80

x = 25

$\hat p$ = x / n =25 / 80 =0.31

P₀ = 0.25

1 - P₀ = 1-0.25 = 0.75

Test statistic = z

= $\hat p$ - P₀ / [$\sqrt$P_{0 *} (1 - P₀ ) / n]

=0.31-0.25/ [$\sqrt$(0.25*0.75) / 80]

= 1.29

Test statistic = z = 1.29

P(z < 1.29) = 0.9015

P-value = 0.9015

$\alpha$ = 0.01

P-value > $\alpha$

0.9015 > 0.01

Fail to reject the null hypothesis .

There is not sufficient evidence to suggest that