Question

I. State null and alternative hypotheses.

II. Decide on the significance level, α.

III. Compute the value of the test statistic.

IV. Determine a p-value, P.

V. If P ≤ α reject H0, otherwise do not reject H0.

VI. Interpret the result of the hypothesis test.

6. A biologist was interested in determining whether specific seedlings treated with a new fertilizer resulted in a higher than average height than the standard height of 11.2 cm. The biologist treated a random sample of 24 seedlings with the fertilizer and subsequently obtained the following heights. Conduct an appropriate hypothesis test using a 5% significance level. Be sure to show all of your work including the calculation of the sample mean and sample standard deviation.

11.5 |
11.8 |
15.7 |
12.1 |
10.1 |
10.5 |

16.5 |
13.5 |
14.4 |
16.7 |
10.9 |
10.0 |

11.1 |
17.1 |
13.3 |
12.4 |
8.5 |
14.3 |

12.9 |
11.1 |
15.0 |
13.3 |
9.9 |
13.5 |

Answer #1

A biologist was interested in determining whether sunflower
seedlings treated with an extract from Vinca minor roots
resulted in a different average height of sunflower seedlings than
the standard height of 15.7 cm at a 0.05 level of significance. The
biologist treated a random sample of n = 33 seedlings with
the extract and subsequently obtained the following heights:
11.5
11.8
15.7
16.1
14.1
10.5
15.2
17.0
12.8
12.4
17.5
13.5
16.5
13.5
14.4
16.7
10.9
13.0
15.1
17.1
13.3...

I. State null and alternative
hypotheses.
II. Decide on the significance level, α.
III. Compute the value of the test
statistic.
IV. Determine the critical
value(s).
V. If the value of the test statistic
falls in the rejection region, reject
H0.
VI. Interpret the result of the hypothesis
test.
Question:
. A manufacturer claims that the thickness of the spearmint gum
it produces is 7.5 one-hundredths of an inch. A quality control
specialist regularly checks this claim. On one production...

*A trainer was interested in determining whether a specially
made shoe resulted in a higher jumping average than the standard of
12.7 inches. The trainer treated a random sample of n = 33 athletes
to use the specialty shoe and subsequently obtained the following
heights:
11.5 11.8 15.7 16.1 14.1 10.5 9.3 15.0 11.1
15.2 19.0 12.8 12.4 19.2 13.5 12.2 13.3
16.5 13.5 14.4 16.7 10.9 13.0 10.3 15.8
15.1 17.1 13.3 12.4 8.5 14.3 12.9 13.5
At 5%...

The cost of electricity (in $) was recorded for a random sample
of 50 cities in a country. These data are as follows:
9.0
9.0
9.5
9.6
10.2
10.8
10.9
11.1
11.4
11.6
11.9
12.3
12.7
12.8
12.9
13.0
13.0
13.5
13.7
13.9
14.1
14.3
14.4
14.7
14.8
14.8
14.9
14.9
15.0
15.1
15.3
15.4
15.7
16.3
16.5
16.6
16.7
16.8
17.1
17.2
17.5
17.8
18.3
18.5
18.7
19.1
19.7
20.2
20.6
21.3
A “less than” frequency distribution is constructed...

Conduct a test at the α=0.05 level of significance by
determining (a) the null and alternative hypotheses, (b) the test
statistic, and (c) the P-value. Assume the samples were obtained
independently from a large population using simple random sampling.
Test whether p 2p1>p2. The sample data are x1=118,
n1=254,x2=134, and n2=303. (a) Choose the correct null and
alternative hypotheses below.
A.
H0: p1=p2 Versus H1: p1
B.
H0: p1=p2 versus H1: p1≠p2
C.
H0: p1=0 versus H1: p1≠0
D.
H0:...

In the following exercise, use a significance level of α = 0.05
to
State a conclusion about the null hypothesis. (Reject
H0 or fail to reject H0 )
Without using technical terms or symbols, state a conclusion
that addresses the original claim.
Original Claim: More than 58% of adults would erase all their
personal information online if they could. The hypothesis test
results in a P-value of 0.3257.

Conduct a test at the α=0.05 level of significance by
determining (a) the null and alternative hypotheses, (b) the test
statistic, and (c) the P-value. Assume the samples were obtained
independently from a large population using simple random sampling.
Test whether p1>p2. The sample data are x1=125, n1=243,x2=139,
and n2=307.
(a) Choose the correct null and alternative hypotheses
below.
A. H0: p1=p2 versus H1: p1>p2
B. H0: p1=0 versus H1: p1≠0
C. H0: p1=p2 Versus H1: p1
D.H0: p1=p2 versus...

Conduct the following test at the α=0.01 level of significance
by determining (a) the null and alternativehypotheses, (b) the
test statistic, and (c) the P-value. Assume that the samples
were obtained independently using simple random sampling.
Test whether p1≠p2. Sample data are x1=30, n1=254, x2=36, and
n2=302.
(a) Determine the null and alternative hypotheses. Choose the
correct answer below.
A. H0: p1=0 versus H1: p1=0
B. H0: p1=p2 versus H1: p1<p2
C. H0: p1=p2 versus H1: p1>p2
D. H0: p1=p2...

Test whether μ1<μ2 at the α = 0.01 level of significance for
the sample data shown in the accompanying table. Assume that the
populations are normally distributed.
Population 1
Population 2
n
33
25
x̅
103.4
114.2
s
12.3
13.3
Determine the null and alternative hypothesis for this test.
B.
H0:μ1=μ2
H1:2μ1<μ2
Determine the P-value for this hypothesis
test.
P-value=__?__
(Round to three decimal places as needed.)

Test whether μ1<μ2 at the alpha α equals =0.01 level of
significance for the sample data shown in the accompanying table.
Assume that the populations are normally distributed.
Population 1
Population 2
n
33
25
x̅
103.4
114.2
s
12.3
13.3
Determine the null and alternative hypothesis for this test.
B.
H0:μ1=μ2
H1:μ1<μ2
Determine the P-value for this hypothesis test.
P=__?__
(Round to three decimal places as needed.)

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