Statistics Fundamentals Unit 5 Challenge 2
Peter wants to test an assumption on the number of trees that tested positive for a
particular infestation. He decides to focus his efforts on examining if more than 12%
of trees have been infested.
What should Peter state for the null hypothesis and alternative hypothesis?
a.)
Null hypothesis:
Alternative hypothesis:
b.)
Null hypothesis:
Alternative hypothesis:
c.)
Null hypothesis:
Alternative hypothesis:
d.)
Null hypothesis:
Alternative hypothesis:
d.)Correct.
Since we are focusing on testing if the proportion of is greater than 12%, we can only
reject the null hypothesis if the value is larger. This would be a one-tailed right test.
So the null hypothesis and alternative hypothesis would be:
Null hypothesis: p = 0.12
Alternative hypothesis: p > 0.12.
A school counselor claims that the average number of sleep students get each night is
6 hours. A researcher has taken a well–designed survey and his sample mean is 8.5
hours and sample standard deviation is 0.25. The sample size is 400.
Which statement is correct?
a.)
The result of the survey is not statistically significant.
, b.)
The result of the survey is statistically significant.
c.)
The difference exists due to chance since the test statistic is small.
d.)
The sample size should be much more.
b.)Correct.
Since we find that 8.5 is much larger than the average 6 hours from a large sample
size and relatively small standard deviation, we can conclude there is a statistically
significant result. It is also practically different as well.
A spice box manufacturing company is having difficulty filling packets to the required
50 grams. Suppose a business researcher randomly selects 60 boxes, weighs each of
them and computes its mean. By chance, the researcher selects packets that have
been filled adequately and that is how he gets the mean weight of 50 g, which falls in
the "fail to reject" region.
The decision is to fail to reject the null hypothesis even though population mean is
NOT actually 50 g.
Which kind of error has the researcher done in this case?
a.)
Type II
b.)
Neither
c.)
Type I
d.)
Both
a.)Correct.
Since the sample evidence provides evidence the null should not be rejected, when
in fact the null hypothesis is false, this is called Type II error.
Which of the following statements is FALSE?
a.)
Expanding the sample size can increase the power of a hypothesis test.
Peter wants to test an assumption on the number of trees that tested positive for a
particular infestation. He decides to focus his efforts on examining if more than 12%
of trees have been infested.
What should Peter state for the null hypothesis and alternative hypothesis?
a.)
Null hypothesis:
Alternative hypothesis:
b.)
Null hypothesis:
Alternative hypothesis:
c.)
Null hypothesis:
Alternative hypothesis:
d.)
Null hypothesis:
Alternative hypothesis:
d.)Correct.
Since we are focusing on testing if the proportion of is greater than 12%, we can only
reject the null hypothesis if the value is larger. This would be a one-tailed right test.
So the null hypothesis and alternative hypothesis would be:
Null hypothesis: p = 0.12
Alternative hypothesis: p > 0.12.
A school counselor claims that the average number of sleep students get each night is
6 hours. A researcher has taken a well–designed survey and his sample mean is 8.5
hours and sample standard deviation is 0.25. The sample size is 400.
Which statement is correct?
a.)
The result of the survey is not statistically significant.
, b.)
The result of the survey is statistically significant.
c.)
The difference exists due to chance since the test statistic is small.
d.)
The sample size should be much more.
b.)Correct.
Since we find that 8.5 is much larger than the average 6 hours from a large sample
size and relatively small standard deviation, we can conclude there is a statistically
significant result. It is also practically different as well.
A spice box manufacturing company is having difficulty filling packets to the required
50 grams. Suppose a business researcher randomly selects 60 boxes, weighs each of
them and computes its mean. By chance, the researcher selects packets that have
been filled adequately and that is how he gets the mean weight of 50 g, which falls in
the "fail to reject" region.
The decision is to fail to reject the null hypothesis even though population mean is
NOT actually 50 g.
Which kind of error has the researcher done in this case?
a.)
Type II
b.)
Neither
c.)
Type I
d.)
Both
a.)Correct.
Since the sample evidence provides evidence the null should not be rejected, when
in fact the null hypothesis is false, this is called Type II error.
Which of the following statements is FALSE?
a.)
Expanding the sample size can increase the power of a hypothesis test.
