Question

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 alternate hypotheses.

*H*_{0}: *p* = 0.75;
*H*_{1}: *p* ≠ 0.75*H*_{0}:
*p* = 0.75; *H*_{1}: *p* >
0.75 *H*_{0}: *p* ≠
0.75; *H*_{1}: *p* =
0.75*H*_{0}: *p* < 0.75;
*H*_{1}: *p* = 0.75*H*_{0}:
*p* = 0.75; *H*_{1}: *p* < 0.75

(b) What sampling distribution will you use?

The Student's *t*, since *np* > 5 and
*nq* > 5.The standard normal, since *np* < 5
and *nq* < 5. The standard normal,
since *np* > 5 and *nq* > 5.The Student's
*t*, since *np* < 5 and *nq* < 5.

What is the value of the sample test statistic? (Round your answer
to two decimal places.)

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

Sketch the sampling distribution and show the area corresponding to
the *P*-value.

(d) Based on your answers in parts (a) to (c), will you reject or
fail to reject the null hypothesis? Are the data statistically
significant at level *α*?

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.

(e) Interpret your conclusion in the context of the
application.

There is sufficient evidence at the 0.05 level to conclude that the true proportion of guests who catch pike over 20 pounds differs from 75%.There is insufficient evidence at the 0.05 level to conclude that the true proportion of guests who catch pike over 20 pounds differs from 75%.

Answer #1

The statistical software output for this problem is:

From above output:

a) Level of significance = 0.05

Hypotheses: *H*0: *p* = 0.75; *H*1:
*p* ≠ 0.75

b) The standard normal, since *np* > 5 and *nq*
> 5.

Test statistic = -1.22

c) P value = 0.2229

d) At the *α* = 0.05 level, we reject the null hypothesis
and conclude the data are statistically significant.

e) There is sufficient evidence at the 0.05 level to conclude that the true proportion of guests who catch pike over 20 pounds differs from 75%.

In a fishing lodge brochure, the lodge advertises that 75% of
its guests catch northern pike over 20 pounds. Suppose that last
summer 64 out of a random sample of 87 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...

In a fishing lodge brochure, the lodge advertises that 75% of
its guests catch northern pike over 20 pounds. Suppose that last
summer 60 out of a random sample of 87 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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its guests catch northern pike over 20 pounds. Suppose that last
summer 59 out of a random sample of 86 guests did, in fact, catch
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population proportion of guests who catch pike over 20 pounds is
different from 75% (either higher or lower)? Use α = 0.05. (a) What
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