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.

Testing a claim about a population mean: t-Test
You work for a steel company that produces "lag bolts". One
product is a 10-inch lag bolt. A recent re-design of a machine
involved in the production of these bolts has the company wondering
whether the production still produces 10-inch lag bolts. You have
gathered a random sample of bolts that have been produced with this
new production process. Conduct an appropriate test, at a 5%
significance level (tα/2=t0.025≈2.1314)(tα/2=t0.025≈2.1314), to
determine if...

1. To give you guided practice in carrying out a hypothesis test
about a population proportion. (Note: This hypothesis test is also
called a z-test for the population proportion.)
2. To learn how to use statistical software to help you carry
out the test.
Background: This activity is based on the
results of a recent study on the safety of airplane drinking water
that was conducted by the U.S. Environmental Protection Agency
(EPA). A study found that out of a...

Test the claim about the population mean μ at the level of
significance α. Assume the population is normally distributed.
Write out null and alternative hypotheses, your critical t-score
and your t-test statistic. Decide whether you would reject or fail
to reject your null hypothesis.
Claim μ ≥ 13.9
α = 0.05
Sample statistics: x̅ = 13, s = 1.3, n = 10
H0:
Ha:
t0:
t-test statistic:
Decision:

Test the claim about the population mean μ at the level of
significance α. Assume the population is normally distributed.
Write out null and alternative hypotheses, your critical z-score
and your z-test statistic. Decide whether you would reject or fail
to reject your null hypothesis.
Claim: μ > 28; α = 0.05, σ = 1.2
Sample statistics: x̅ = 28.3, n = 50
H0:
Ha:
Critical z-score:
Z test statistic:
Decision:

Your friend tells you that the proportion of active Major League
Baseball players who have a batting average greater than .300 is
different from 0.71, a claim you would like to test. The hypotheses
for this test are Null Hypothesis: p = 0.71, Alternative
Hypothesis: p ≠ 0.71. If you randomly sample 23 players and
determine that 14 of them have a batting average higher than .300,
what is the test statistic and p-value?

Your friend tells you that the proportion of active Major League
Baseball players who have a batting average greater than .300 is
different from 0.64, a claim you would like to test. The hypotheses
for this test are Null Hypothesis: p = 0.64, Alternative
Hypothesis: p ≠ 0.64. If you randomly sample 30 players and
determine that 24 of them have a batting average higher than .300,
what is the test statistic and p-value?

Your friend tells you that the proportion of active Major League
Baseball players who have a batting average greater than .300 is
different from 0.77, a claim you would like to test. The hypotheses
for this test are Null Hypothesis: p = 0.77, Alternative
Hypothesis: p ≠ 0.77. If you randomly sample 24 players and
determine that 19 of them have a batting average higher than .300,
what is the test statistic and p-value?
Question 9 options:
1)
Test Statistic:...

Part 1 Hypothesis Test and Confidence Interval from 1 sample
Test ONE claim about a population parameter by collecting your
own data or using our class survey data. Include your
written claim, hypothesis in both
symbolic and written form, relevant statistics
(such as sample means, proportions etc.), test
statistic, p-value (or critical value),
conclusion, and interpretation of
your conclusion in the context of your claim. Use a 0.05
significance level.
You will also construct a 95% confidence interval
estimate of...

Your friend tells you that the proportion of active Major League
Baseball players who have a batting average greater than .300 is
different from 0.74, a claim you would like to test. The hypotheses
here are Null Hypothesis: p = 0.74, Alternative Hypothesis: p ≠
0.74. If you take a random sample of players and calculate p-value
for your hypothesis test of 0.9623, what is the appropriate
conclusion? Conclude at the 5% level of significance.
Question 15 options:
1)
We...

Your task is to pick a hypothesis to test about a population
proportion (section 8.2) or a population mean (section 8.3). Once
you have determined your hypothesis you must go and collect the
data. Make sure your sample meets the requirements of a test
presented in sections 8.2 and 8.3 (such as appropriate sample
size). Use a 0.05 significance level.
Please clearly state the null and alternative hypotheses in
symbolic form and in words. State any relevant statistics from your...

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