Question

A random sample of 20 binomial trials resulted in 8 successes. Test the claim that the population proportion of successes does not equal 0.50. Use a level of significance of 0.05.

(a) Can a normal distribution be used for the *p̂*
distribution? Explain.

Yes, *np* and *nq* are both greater than 5.No,
*np* and *nq* are both less than
5. No, *np* is greater than 5, but
*nq* is less than 5.Yes, *np* and *nq* are
both less than 5.No, *nq* is greater than 5, but *np*
is less than 5.

(b) State the hypotheses.

*H*_{0}: *p* < 0.5;
*H*_{1}: *p* = 0.5*H*_{0}:
*p* = 0.5; *H*_{1}: *p* <
0.5 *H*_{0}: *p* =
0.5; *H*_{1}: *p* >
0.5*H*_{0}: *p* = 0.5;
*H*_{1}: *p* ≠ 0.5

(c) Compute *p̂*.

Compute the corresponding standardized sample test statistic.
(Round your answer to two decimal places.)

(d) Find the *P*-value of the test statistic. (Round your
answer to four decimal places.)

(e) Do you reject or fail to reject

*H*_{0}?

Explain.

At the *α* = 0.05 level, we reject the null hypothesis
and conclude the data are statistically significant.At the
*α* = 0.05 level, we reject the null hypothesis and conclude
the data are not statistically
significant. At the *α* = 0.05 level,
we fail to reject the null hypothesis and conclude the data are
statistically significant.At the *α* = 0.05 level, we fail
to reject the null hypothesis and conclude the data are not
statistically significant.

(f) What do the results tell you?

The sample *p̂* value based on 20 trials is sufficiently
different from 0.50 to not reject *H*_{0} for
*α* = 0.05.The sample *p̂* value based on 20 trials
is sufficiently different from 0.50 to justify rejecting
*H*_{0} for *α* =
0.05. The sample *p̂* value based on
20 trials is not sufficiently different from 0.50 to not reject
*H*_{0} for *α* = 0.05.The sample *p̂*
value based on 20 trials is not sufficiently different from 0.50 to
justify rejecting *H*_{0} for *α* = 0.05.

Answer #1

A random sample of 20 binomial trials resulted in 8 successes.
Test the claim that the population proportion of successes does not
equal 0.50. Use a level of significance of 0.05.
(a) Can a normal distribution be used for the p hat
distribution? Explain.
No, n·p and n·q are both less than 5.
No, n·p is greater than 5, but n·q is less than 5.
No, n·q is greater than 5, but n·p is less than 5.
Yes, n·p and...

A random sample of 30 binomial trials resulted in 12 successes.
Test the claim that the population proportion of successes does not
equal 0.50. Use a level of significance of 0.05.
(a) Can a normal distribution be used for
the distribution? Explain.
Yes, n·p and n·q are both greater than 5
.No, n·p and n·q are both less than
5.
Yes, n·p and n·q are both less than 5
.No, n·p is greater than 5, but n·q is less
than 5....

A random sample of 50 binomial trials resulted in 20 successes.
Test the claim that the population proportion of successes does not
equal 0.50. Use a level of significance of 0.05.
(e)
Do you reject or fail to reject H0?
Explain.
At the α = 0.05 level, we reject the null hypothesis and
conclude the data are statistically significant.At the α = 0.05
level, we reject the null hypothesis and conclude the data are not
statistically significant. At the α =...

A random sample of 20 binomial trials resulted in 8 successes.
Test the claim that the population proportion of successes does not
equal 0.50. Use a level of significance of 0.05. (a) Can a normal
distribution be used for the distribution? Explain. Yes, n·p and
n·q are both less than 5. No, n·p is greater than 5, but n·q is
less than 5. Yes, n·p and n·q are both greater than 5. No, n·p and
n·q are both less than...

For one binomial experiment,
n1 = 75
binomial trials produced
r1 = 30
successes. For a second independent binomial
experiment,
n2 = 100
binomial trials produced
r2 = 50
successes. At the 5% level of significance, test the
claim that the probabilities of success for the two binomial
experiments differ.
(a) Compute the pooled probability of success for the
two experiments. (Round your answer to three decimal
places.)
(b) Check Requirements: What distribution does the
sample test statistic follow? Explain....

For one binomial experiment,
n1 = 75
binomial trials produced
r1 = 45
successes. For a second independent binomial experiment,
n2 = 100
binomial trials produced
r2 = 65
successes. At the 5% level of significance, test the claim that
the probabilities of success for the two binomial experiments
differ.(a) Compute the pooled probability of success for the two
experiments. (Round your answer to three decimal places.)
(b) Check Requirements: What distribution does the sample test
statistic follow? Explain.
The...

For one binomial experiment, n1 = 75 binomial trials produced r1
= 30 successes. For a second independent binomial experiment, n2 =
100 binomial trials produced r2 = 50 successes. At the 5% level of
significance, test the claim that the probabilities of success for
the two binomial experiments differ. (a) Compute the pooled
probability of success for the two experiments. (Round your answer
to three decimal places.) (b) Check Requirements: What distribution
does the sample test statistic follow? Explain....

For one binomial experiment, n1 = 75 binomial trials
produced r1 = 45 successes. For a second independent
binomial experiment, n2 = 100 binomial trials produced
r2 = 65
successes. At the 5% level of significance, test the claim that
the probabilities of success for the two binomial experiments
differ.
(a)
Compute the pooled probability of success for the two
experiments. (Round your answer to three decimal places.)
(b)
Check Requirements: What distribution does the sample test
statistic follow? Explain....

The following is based on information from The Wolf in the
Southwest: The Making of an Endangered Species, by David E.
Brown (University of Arizona Press). Before 1918, the proportion of
female wolves in the general population of all southwestern wolves
was about 50%. However, after 1918, southwestern cattle ranchers
began a widespread effort to destroy wolves. In a recent sample of
37 wolves, there were only 11 females. One theory is that male
wolves tend to return sooner than...

In a fishing lodge brochure, the lodge advertises that 75% of
its guests catch northern pike over 20 pounds. Suppose that last
summer 56 out of a random sample of 81 guests did, in fact, catch
northern pike weighing over 20 pounds. Does this indicate that the
population proportion of guests who catch pike over 20 pounds is
different from 75% (either higher or lower)? Use α =
0.05.
(a) What is the level of significance?
State the null and...

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