Question

1. A researcher wishes to assess the impact of a new medication in decreasing blood glucose levels. The standard success rate for blood glucose medications is 93.7%. Of the 1,000 participants in his study, 948 indicated lowered blood glucose levels as a result of taking the new medication.

Is the new medication more effective in lowering blood glucose levels? Run the appropriate test at the 5% level of significance.

Step 1.           Set up hypotheses and determine level of significance

Step 2.            Select the appropriate test statistic

                                             

Step 3.            Set up decision rule

                       

Step 4.            Compute the test statistic

                               

Step 5.            Conclusion

Answer 1

Solution :

This is the two tailed test .

The null and alternative hypothesis is

H₀ : p = 0.937

H_a : p 0.937

n = 1000

x = 948

= x / n = 948 / 1000 = 0.948

P₀ = 0.937

1 - P₀ = 0.063

z = - P₀ / [P_{0 *} (1 - P₀ ) / n]

= 0.948 - 0.937 / [(0.937 * 0.063) / 1000]

= 1.43

Test statistic = 1.43

P(z > 1.43) = 1 - P(z < 1.43) = 0.0764

P-value = 2 * 0.0764 = 0.1527

= 0.05

P-value >

Fail to reject the null hypothesis .

There is sufficient evidence to the new medication more effective in lowering blood glucose levels .