Question

Suppose someone tells you they know that thumbtacks land up 70% of the time. You throw 50 thumbtacks in the air, and find that 41 of them land pointing up. Use the sample collected to conduct a hypothesis test with an α = 0.05 significance level to test the validity of the claim. Be sure to check the conditions of the test and state your conclusion in context.

Answer 1

(a)

H0: Null Hypothesis: p =.0.70 ( Thumbtacks land up 70% of the time ) (Claim)

HA: Alternative Hypothesis: p .0.70 ( Thumbtacks do not land up 70% of the time )

n = 50

= 41/50 =0.82

= 0.05

From Table, critical values of Z = 1.96

Test Statistic is given by:

Since calculated value of Z = 1.852 is less than critical value of Z = 1.96, the difference is not significant. Fail to reject null hypothesis.

Conclusion:
The data support the claim that thumbtacks land up 70% of the time.

(b)

Conditions of the test are satisfied as follows:
(i) The data are Simple Random Sample from the population of interest

(ii) The population isat least 10 times as large as the sample

(iii) np = 50 X 0.70 = 35 >10

n (1 - p) = 50 X 0.30 = 15 > 10

So,

All conditions are satisfied,

(c)

Our conclusion:

The data support the claim that thumbtacks land up 70% of the time