Question

Consider the following scenario: An industrial seller of grass seeds packages its product in 50-pound bags. A customer has recently filed a complained alleging that the bags are underfilled. A production manager randomly samples a batch and measures the following weights:

Weight, (lbs)

45.6 49.5

47.7 46.7

47.6 48.8

50.5 48.6

50.2 51.5

46.9 50.2

47.8 49.9

49.3 49.8

53.1 49.3

49.5 50.1

To determine whether the bags are indeed being underfilled by the machinery, the manager must conduct a test of mean with a significance level α = 0.05.

- State appropriate null (Ho) and alternative (H1) hypotheses.
- What is the critical value if we work with a significant level α = 0.05?
- What is the decision rule?
- Calculate the test statistic.
- Are the bags indeed being underfilled?

Answer #1

A gardener plants 300 sunflower seeds (of a brand called
KwikGrow) and, after 2 weeks, measures the seedlings’ heights (in
mm). These height are: 38.6 39.1 50.4 49.2 46.2 0 43.1 49.6 16.1
17.9 11.6 50.2 36.5 50.6 40.3 36.3 14.3 40.8 12.1 43.7 47.2 49.9
37.9 49.1 53 47.7 13.8 38.3 49.2 50.6 49.6 52.3 19.8 12.8 46.9 35.3
38.7 39.3 12.4 51.9 36.9 20.8 51.7 44.3 49.1 10.7 14.9 48.2 14.8 38
41.4 39.4 11.9 13.8 0 35.1...

A gardener plants 300 sunflower seeds (of a brand called
KwikGrow) and, after 2 weeks, measures the seedlings’ heights (in
mm). These heights are recorded in the file Sunflower.csv. He is
interested in testing whether the mean height of sunflowers grown
from KwikGrow seeds is greater than 33 mm two weeks after planting.
He decides to conduct a hypothesis test by assuming that the
sampling distribution of the sample mean has a normal distribution.
For the purposes of this question,...

5. As part of the efforts to remain competitive, Engine-X tries
to keep up with the latest in production technology. The company
spends a great deal of effort testing new technologies for its
sports engine division where competition is high. When a new
technology is first introduced, firms often experience learning,
resulting in a gradual decrease in the time required to produce
successive units. Generally, the rate of improvement declines until
production time levels off. On typical example is the...

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