Question

14.) A private study group from Tanzania claims that only 29% of its citizens are opposed to continued quarantine measures. The government claims that the percentage is much higher. Another private study group decides to test the governments claim by selecting a random sample of 81 Tanzanian residents. They find that 29 of them are opposed to continued quarantine measures.

a.) What is the variable? Is it an attribute or measurable?

b.) State the hypothesis.

c.) Calculate both the p-value and the value of the test statistic.

d.) Would you reject H0 or fail to reject H0 at a 5% level of significance?

e.) What would you conclude about the Tanzanian government's claim?

Answer 1

Solution :

This is the right tailed test .

The null and alternative hypothesis is

H0 : p = 0.29

Ha : p > 0.29

n =81

x =29

= x / n = 29 / 81 = 0.36

P0 = 0.29

1 - P0 = 1 - 0.29 =0.71

Test statistic = z

= - P0 / [P0 * (1 - P0 ) / n]

=0.36 -0.29 / [(0.29*0.71) / 81]

= 1.39

Test statistic = z =1.39

P(z > 1.39 ) = 1 - P(z < 1.39 ) = 1 - 0.9177

P-value = 0.0823

= 0.05

P-value >

0.0823 >0.05

Fail to reject the null hypothesis .

There is insufficient evidence to suggest that