Question

You are conducting a study to see if the proportion of voters who prefer Candidate A is significantly more than 47%. With Ha : p > 47% you obtain a test statistic of z = 1.997. Find the p-value accurate to 4 decimal places. p-value =

You are conducting a study to see if the accuracy rate for fingerprint identification is significantly less than 0.62. Thus you are performing a left-tailed test. Your sample data produce the test statistic z = − 2.853. Find the p-value accurate to 4 decimal places. p-value =

The Dean of ASBE School of Business is concerned that grades in the MBA program are distributed appropriately. Too many high grades or too many low grades would pose a problem. We wish to test the claim that the mean GPA of ASBE students is smaller than 3.3 at the .05 significance level. The null and alternative hypothesis would be: H 0 : μ = 3.3 H a : μ ≠ 3.3 H 0 : p = 3.3 4 H a : p < 3.3 4 H 0 : μ = 3.3 H a : μ > 3.3 H 0 : μ = 3.3 H a : μ < 3.3 H 0 : p = 3.3 4 H a : p > 3.3 4 H 0 : p = 3.3 4 H a : p ≠ 3.3 4 Correct The test is: left-tailed right-tailed two-tailed Correct Based on a sample of 50 student grades, the sample mean GPA was 3.29 with a standard deviation of 0.06 The test statistic is: Incorrect (Round to 3 decimals) Based on this we: Reject the null hypothesis Fail to reject the null hypothesis

Answer 1

You are conducting a study to see if the proportion of voters who prefer Candidate A is significantly more than 47%. With % you obtain a test statistic of . Find the p-value.

SOLUTION:

The z test statistic is . And the alternative hypothesis given is that the proportion of voters who prefer Candidate A is significantly more than 47%. Thus the given problem is right tailed test.

Let us round off the z statistic value into two decimal places

The p value for the given problem is,

(Since }

Using the z table, the probability value is the value with corresponding row 2.0 and column 0.00.

  

Thus the p value is .

You are conducting a study to see if the accuracy rate for fingerprint identification is significantly less than . Thus you are performing a left-tailed test. Your sample data produce the test statistic .

SOLUTION:

Since the given problem is left tailed test, the p value is,

Using the z table, the probability value is the value with corresponding row -2.8 and column 0.05.

Thus the p value is

The Dean of ASBE School of Business is concerned that grades in the MBA program are distributed appropriately. Too many high grades or too many low grades would pose a problem. We wish to test the claim that the mean GPA of ASBE students is smaller than 3.3 at the .05 significance level.

HYPOTHESIS:

The null and alternate hypothesis is:

(That is, the mean GPA of ASBE students is not significantly different from 3.3 )

(That is, the mean GPA of ASBE students is smaller than 3.3 )

Since the alternative hypothesis is , the correct test is left-tailed test.

TEST STATISTIC:

Given the sample size , sample mean and sample standard deviation , the t test statistic is,

CRITICAL VALUE:

The left tailed t critical value at significance level with degrees of freedom is .

DECISION RULE:

CONCLUSION:

Since the calculated t test statistic (-1.178) is greater than the t critical value (-1.677), we fail to reject null hypothesis and conclude that the mean GPA of ASBE students is not significantly different from 3.3.