Question

A researcher claims that 85% percent of American think they are unlikely to contract the Zika virus. In a random sample of 300 Americans, 225 think they are unlikely to control the Zika virus. At 5% level of significance, is there enough evidence to reject the researcher's claim?

What is the Null hypothesis (H0); Alternate hypothesis (H1); and the direction of the test?

Which distribution is used in this case?

What is the critical value?

What is the Test Statistic Value?

What is the P-value?

What is the conclusion of the test?

Answer 1

Sample size, n= 300

Sample proportion of Americans who think they are unlikely to contract the Zika virus, = 225/300 = 0.75

(a) Null hypothesis: p=0.85 (Claim)

Alternate hypothesis: p not= 0.85

(b) Z- distribution will be used in this case.

(c) Critical Values, Z(0.05/2) = -1.96 & 1.96

(d) Test statistic = = = -4.85

(e) P- Value = 2 P( z < -4.85)

= 2 { 1- P(z < 4.85) }

= 2 { 1 - 0.9999}

= 2 *0.0001

= 0.0002

(f) Since the P-Value is less than the significance level (0.05) , we will reject the null hypothesis.

Hence we do have enough evidence to reject the researcher's claim.