Question

the percentage of deaths due to disease is 12.5%. A medical student wants to test whether the percentage of deaths due to disease is less than 12.5%. She collected data on deaths due to disease over 8 states. She found out that there were 102 patients diagnosed with disease and 11 patients died. Carry out a test of significance by answering the questions below in as much detail as possible. Use a 10% level of significance. What is the value of the test statistic? (Hint: Round sample proportion to four decimal places.) Question 2 options: A) -0.53 B) 0.53 C) 0.01 D) -0.01 E) -0.05

Answer 1

Solution:

Given:

A medical student wants to test whether the percentage of deaths due to disease is less than 12.5%.

p = population proportion of deaths due to disease = 0.125

n = Sample size = 102

x = Number  of deaths due to disease 11

Thus sample proportion of deaths due to disease is:

Hypothesis of the study are:

H0: p = 0.125

Vs

H1: p < 0.125

Find test statistic value:

Find z critical value at 10% level of significance.

Look in z table for Area= 0.1000 or its closest area and find z value.

Area 0.1003 is closest to 0.1000 and it corresponds to -1.2 and 0.08

Thus z = -1.28

Decision Rule:

Reject null hypothesis ,if z test statistic value < z critical value , otherwise we fail to reject H0.

Since z test statistic value = - 0.53 > z critical value , we failed to reject H0.

Conclusion:

There is not sufficient evidence to conclude that:  the percentage of deaths due to disease is less than 12.5%