Question

QUESTION 4

1. In a sample of 110 university lecturers, 96 said that mathematic courses in high school were the most important source of a student’s success in engineering departments. Test the hypothesis that mathematic courses are the most important sources of a child’s success for at least 79% of university lecturers against the alternative that the population percentage is less than 79%. Use a=0.05.

   a. Construct hypthesis H₀: vs H₁: (IMPORTANT: for inequalities use one of the appropriate of the following. For example; x less than y, x greater than y, x greater than or equal to y, x less than or equal to y )       

   b. Test statistic value is

   c. P-value is

   d. Decision  (here use "reject" or "fail to reject", but don't forget to explain on the paper!)

Answer 1

Let p be the population percentage for people believing mathematics course are the most important sources of a child success

a)

Hypotheses Statements are

Ho: p >= 0.79 [ p is greater than or equal to 0.79]

Ha: p <  0.79 [ p is less than 0.79]

b)

Sample Proportion,

Test statistics (z value )

c)

p-value

For the test statistic, z = 2.13, and left-tailed test, the p-value is 0.9834

d)

Decision Rule

If the p-value is less than alpha (0.05), we reject the null.

Here p-value is greater than alpha, So we fail to reject the null