M7A2 6 points 1. How long do new batteries last on a camping trip? A random sample of n1 = 42 small

M7A2
6 points
1.
How long do new batteries last on a camping trip? A random
sample of n1 = 42 small camp flashlights were installed with brand I batteries
and left on until the batteries failed. The sample mean lifetime was x1 = 9.8
hours with sample standard deviation s1 = 2.2 hours. Another random sample of
n2 = 38 small flashlights of the same model were installed with brand II
batteries and left on until the batteries failed. The sample mean of lifetimes
was x2 = 8.1 hours with sample standard deviation s2 = 3.5 hours.
1.
Should you use the critical value (zc) or (tc) in determining a
confidence interval in this problem? Explain.
2.
Find a 90% confidence interval for the population difference m1
– m2 of lifetimes for these batteries.
3.
Does the confidence interval in part (b) contain all positive,
all negative, or both positive and negative numbers? What does this tell you
about the mean life of battery I compared to battery II?
2.
Two pain relief drugs are being considered. A random sample of 8
doses of the first drug showed that the average amount of time required before
the drug was absorbed into the bloodstream was x1 = 24 minutes with population
standard deviation = 4 minutes. For the second drug, a random sample of 10
doses showed the average time required for absorption was x2 = 29 minutes with
population standard deviation = 3.9 minutes. Assume the absorption times follow
a normal distribution.
1.
Should you use the critical value (zc) or (tc) in determining a
confidence interval in this problem? Explain.
2.
Find a 90% confidence interval for the difference in average
absorption time for the two drugs.
3.
Does it appear that one drug is absorbed faster than the other
(at the 90% level)? Explain.This is the first assignment to be submitted
for module 7. I do expect to see how you work out the calculations in these
problems. Due to the calculations involved, it may be easier to print the
assignment and scan and upload as pdf files. You may upload up to 10 files.
Another option is to take a digital photograph of the pages with the work
completed and email or upload the pictures.MAT 151M7A115 Points1.
Collette is self-employed, selling items at Home Interior
parties. She wants to estimate the average amount a client spends at each
party. A random sample of 35 clients’ receipts gave a sample mean of $34.70
with population standard deviation $4.85. 1.
Should you use the critical value (zc) or (tc) in determining a
confidence interval in this problem? Explain. 2.
Find a 90% confidence interval for the average amount expected
to be spent by an individual. 3.
Write a brief expanation of the meaning of the confidence
interval in the context of this problem 4.
For a party with 35 clients, use part (b) to estimate a range of
dollar values for Collette’s total sales at that party. 2.
How long does it take to commute from home to work? It depends
on several factors including route, traffic, and time of departure. The data
below are normally distributed results (in minutes) from a random sample of 8
trips.

27

38

30

42

24

37

30

39

1.
Using technology, determine the mean for this data. 2.
Using technology, determine the standard deviation for this
data. 3.
Should you use the critical value (zc) or (tc) in determining a
confidence interval in this problem? Explain. 4.
Use these data to create a 95% confidence interval for the
population mean time of the commute. 3.
A random sample of 53 students were asked for the number of
semester hours they are taking this semester at Surry Community College. The
sample standard deviation was found to be s = 4.7 semester hours. How many more
students should be included in the sample to be 99% sure the sample mean is
within one semester hour of the population mean for all students at this
college? (Hint: the margin of error is the amount added or subtracted from the
mean.)4.
How long do new batteries last on a camping trip? A random
sample of n1 = 42 small camp flashlights were installed with brand I batteries
and left on until the batteries failed. The sample mean lifetime was x1 = 9.8
hours with sample standard deviation s1 = 2.2 hours. Another random sample of
n2 = 38 small flashlights of the same model were installed with brand II
batteries and left on until the batteries failed. The sample mean of lifetimes
was x2 = 8.1 hours with sample standard deviation s2 = 3.5 hours. 1.
Should you use the critical value (zc) or (tc) in determining a
confidence interval in this problem? Explain. 2.
Find a 90% confidence interval for the population difference m1
– m2 of lifetimes for these batteries. 3.
Does the confidence interval in part (b) contain all positive,
all negative, or both positive and negative numbers? What does this tell you
about the mean life of battery I compared to battery II? 5.
Two pain relief drugs are being considered. A random sample of 8
doses of the first drug showed that the average amount of time required before
the drug was absorbed into the bloodstream was x1 = 24 minutes with population
standard deviation = 4 minutes. For the second drug, a random sample of 10
doses showed the average time required for absorption was x2 = 29 minutes with
population standard deviation = 3.9 minutes. Assume the absorption times follow
a normal distribution. 1.
Should you use the critical value (zc) or (tc) in determining a
confidence interval in this problem? Explain. 2.
Find a 90% confidence interval for the difference in average
absorption time for the two drugs. 3.
Does it appear that one drug is absorbed faster than the other
(at the 90% level)? Explain

 

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