Question

A marketing consultant was hired to visit a random sample of five sporting goods stores across the state of California. Each store was part of a large franchise of sporting goods stores. The consultant taught the managers of each store better ways to advertise and display their goods. The net sales for 1 month before and 1 month after the consultant's visit were recorded as follows for each store (in thousands of dollars):

Store |
1 |
2 |
3 |
4 |
5 |

Before
visit |
57.3 | 94.4 | 49.2 | 77.4 | 43.2 |

After
visit |
63.3 | 101.6 | 57.8 | 81.2 | 41.9 |

Do the data indicate that the average net sales improved? Use
*α* = 0.05. (Let *d* = before − after.)

What are we testing in this problem?

single proportionpaired difference difference of proportionsdifference of meanssingle mean

What is the level of significance?

State the null and alternate hypotheses.

*H*_{0}: *μ*_{d} = 0;
*H*_{1}: *μ*_{d} ≠
0*H*_{0}: *μ*_{d} ≠ 0;
*H*_{1}: *μ*_{d} =
0 *H*_{0}:
*μ*_{d} > 0; *H*_{1}:
*μ*_{d} ≤ 0*H*_{0}:
*μ*_{d} ≥ 0; *H*_{1}:
*μ*_{d} < 0

What sampling distribution will you use? What assumptions are you
making?

The standard normal. We assume that *d* has an
approximately normal distribution.The Student's *t*. We
assume that *d* has an approximately uniform
distribution. The standard normal. We assume
that *d* has an approximately uniform distribution.The
Student's *t*. We assume that *d* has an
approximately normal distribution.

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

Estimate the *P*-value.

*P*-value > 0.2500.125 < *P*-value <
0.250 0.050 < *P*-value <
0.1250.025 < *P*-value < 0.0500.005 <
*P*-value < 0.025*P*-value < 0.005

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

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.

Interpret your conclusion in the context of the application.

There is sufficient evidence at the 0.05 to conclude that the average net sales have improved.There is insufficient evidence at the 0.05 to conclude that the average net sales have improved.

Answer #1

paired difference

level of significance =0.05

*μ*_{d} ≥ 0; *H*_{1}:
*μ*_{d} < 0

.The Student's *t*. We assume that *d* has an
approximately normal distribution.

**sample test statistic = -2.810**

**0.005 < P-value < 0.025**

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

There is sufficient evidence at the 0.05 to conclude that the average net sales have improved.

A marketing consultant was hired to visit a random sample of
five sporting goods stores across the state of California. Each
store was part of a large franchise of sporting goods stores. The
consultant taught the managers of each store better ways to
advertise and display their goods. The net sales for 1 month before
and 1 month after the consultant's visit were recorded as follows
for each store (in thousands of dollars):
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2
3
4
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A marketing consultant was hired to visit a random sample of
five sporting goods stores across the state of California. Each
store was part of a large franchise of sporting goods stores. The
consultant taught the managers of each store better ways to
advertise and display their goods. The net sales for 1 month before
and 1 month after the consultant's visit were recorded as follows
for each store (in thousands of dollars):
Store
1
2
3
4
5
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