Question

Testing a claim about a population proportion: 1PropZTest

You have a friend that loves to brag about "mad bottle flipping skills." Yesterday, he said to you, "Dude, I can flip a bottle and make it land correctly 9 out of 10 times!" You suspect that his proportion is actually much lower. You put him to the test, and 173 flips out of 200 land upright. Carry out a hypothesis test, at a 5% level of significance, to test your friend's claim.

a) State the parameter of interest. Write out the null and alternate hypothesis.

b) Are the necessary conditions present to carry out this inference procedure? Explain in context.

c) Carry out the procedure ("crunch the numbers"):

Sample proportion:

Standard deviation of sample proportion:

Standardized test statistic:

P-value:

d) Should the null hypothesis be rejected? (Enter "yes" or "no".)

Write a conclusion in context.

Answer 1

Solution:-

a) The parameter of interest is proportion of flipping a bottle and landing it correcty.

b) Yes, all nececcarry conditions are met, number of success and failure are greater than 10 and each event is independent from the other.

State the hypotheses. The first step is to state the null hypothesis and an alternative hypothesis.
Null hypothesis: P = 0.90
Alternative hypothesis: P < 0.90
Note that these hypotheses constitute a one-tailed test. The null hypothesis will be rejected only if the
sample proportion is too small.
Formulate an analysis plan. For this analysis, the significance level is 0.05. The test method, shown in
the next section, is a one-sample z-test.
Analyze sample data. Using sample data, we calculate the standard deviation (S.D) and compute the z-
score test statistic (z).

c)

S.D = sqrt[ P * ( 1 - P ) / n ]
S.D = 0.02121
z = (p - P) / S.D
z = -1.65
where P is the hypothesized value of population proportion in the null hypothesis, p is the sample
proportion, and n is the sample size.
Since we have a one-tailed test, the P-value is the probability that the z-score is less than -1.65.
Thus, the P-value = 0.049
Interpret results. Since the P-value (0.049) is less than the significance level (0.05), we cannot accept the
null hypothesis.

d)

Reject the null hypothesis.
From the above test we have sufficient evidence in the favor of the claim that proportion is actually much lower.