Question

In this problem, assume that the distribution of differences is
approximately normal. *Note*: For degrees of freedom
*d*.*f*. not in the Student's *t* table, use
the closest *d*.*f*. that
is *smaller*. In some situations, this choice of
*d*.*f*. may increase the *P*-value by a small
amount and therefore produce a slightly more "conservative"
answer.

The artifact frequency for an excavation of a kiva in Bandelier
National Monument gave the following information.

Stratum |
Flaked Stone
Tools |
Nonflaked Stone
Tools |

1 | 9 | 2 |

2 | 10 | 4 |

3 | 7 | 3 |

4 | 1 | 3 |

5 | 4 | 7 |

6 | 38 | 32 |

7 | 51 | 30 |

8 | 25 | 12 |

Does this information indicate that there tend to be more flaked
stone tools than nonflaked stone tools at this excavation site? Use
a 5% level of significance. (Let *d* = flaked −
nonflaked.)

(a) What is the level of significance?

State the null and alternate hypotheses. Will you use a
left-tailed, right-tailed, or two-tailed test?

*H*_{0}: *μ*_{d} = 0;
*H*_{1}: *μ*_{d} ≠ 0;
two-tailed*H*_{0}: *μ*_{d} =
0; *H*_{1}: *μ*_{d} < 0;
left-tailed *H*_{0}:
*μ*_{d} = 0; *H*_{1}:
*μ*_{d} > 0;
right-tailed*H*_{0}: *μ*_{d}
> 0; *H*_{1}: *μ*_{d} =
0; right-tailed

(b) What sampling distribution will you use? What assumptions are
you making?

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

(c) Find (or 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.

(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 fail to reject the null
hypothesis and conclude the data are not statistically
significant.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.

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

Reject the null hypothesis, there is insufficient evidence to claim that the average number of flaked stone tools is higher.Reject the null hypothesis, there is sufficient evidence to claim that the average number of flaked stone tools is higher. Fail to reject the null hypothesis, there is sufficient evidence to claim that the average number of flaked stone tools is higher.Fail to reject the null hypothesis, there is insufficient evidence to claim that the average number of flaked stone tools is higher.

Answer #1

a)

0.05 is alpha

H0: μd = 0; H1: μd > 0; right-tailed

b)

We assume that d has an approximately normal distribution.

Test statistic,

t = (dbar - 0)/(s(d)/sqrt(n))

t = (6.5 - 0)/(7.7644/sqrt(8))

t = 2.368

c)

P-value Approach

P-value = 0.0249

0.125 < P-value < 0.250

As P-value < 0.05, reject the null hypothesis.

d)

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

e)

Reject the null hypothesis, there is sufficient evidence to claim that the average number of flaked stone tools is higher.

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approximately normal. Note: For degrees of freedom
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