Question

Algebra students in a local high school use a computer-based program to brush up on algebra skills to be assessed by a test. The program claims that 80% of students using the program will pass the test. After an early pilot of the new program, only 34 of 50 student passed the test A 1-proportion z test is going to be conducted to see if there's evidence that the true passing rate is less than what was claimed. The null hypothesis is p= 0.80. (a) What is the alternative hypothesis? H p 0.80 OH: p < 0.80 Ha p 0.80 Ha p 0.80 (b) What is the value of z, the test statistic? (Round your answer to two decimal places.) z= (c) What is the P-value? (Use a table or technology. Round your answer to four decimal places.)

Answer 1

This is the left tailed test .

The null and alternative hypothesis is ,

H₀ : p =0.80

H_a : p <0.80

$\hat p$ = x / n = 34/50=0.68

P₀ = 0.80

1 - P₀ = 1-0.80=0.20

Test statistic = z

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

= 0.68-0.80/ [$\sqrt$(0.80*0.20) / 50]

= -2.12

P(z < -2.12) = P(z < -2.12) =0.0170

P-value = 0.0170