Statistics

 

#1 (CH. 8.4) The National Health Statistics Reports described a study in which a sample of 401
one year old baby boys were weighed. Their mean weight was 25.5 pounds with a standard deviation of
4.1 pounds. A pediatrician claims that the mean weight of one-year-old boys is equal to 25 pounds.
Use a 0.01 significance level to test his claim. Do the results of this test support the claim?
• Write the claim using one of the following symbols (< or ≥ or > or ≤ or = or ≠):

• Write the claim again using the opposite symbol:

• Label each statement.

o (null hypothesis):
o (alternative hypothesis):

• Write down the value given for the significance level:

• Write the Critical value (the Table value) here:
• Now use your calculator or the formula to tell me the calculated value (known as the “test
statistic”):
• REJECT : YES or NO

• What is your conclusion?
#2 (CH. 8.4) In a study to determine whether counseling could help people lose weight, a
sample of people experienced a group-based behavioural intervention, which involved weekly meetings
with a specialist over a period of six months. The following data are the numbers of pounds lost by 12
people in the study:

18.2 33.8 20.0 8.8
17.3 3.9 8.5 19.3
24.8 29.7 17.1 13.4

Use this data and a 0.05 significance level to test the claim that the average weight loss is
greater than 10 pounds.

• Write the claim using one of the following symbols (< or ≥ or > or ≤ or = or ≠):

• Write the claim again using the opposite symbol:

• Label each statement.

o (null hypothesis):
o (alternative hypothesis):

• Write down the value given for the significance level:

• Write the Critical value (the Table value) here:
• What is the calculated mean:
• What is the calculated standard deviation:
• Now use your calculator or the formula to tell me the calculated value (known as the “test
statistic”):
• REJECT : YES or NO

• What is your conclusion?
#3 (Ch. 9-2) In a study conducted for an experimental nasal spray vaccine, it was found that 45 of
the 850 who received the vaccine got the flu compared to the 95 out of 1232 who received the placebo
got the flu. Construct a 90% confidence interval estimate for the DIFFERENCE between the two groups.
a. What is the Critical Value from the TABLE:

b. What is the calculated Confidence Interval:
c. Does the interval show there is a difference between the two groups?
#4 (CH. 9-2) Use the data from problem #3 and a 0.10 significance level to test the claim that
there IS A DIFFERENCE between the two groups. Does your result here support the results from problem
#3?

• Write the claim using one of the following symbols (< or ≥ or > or ≤ or = or ≠):

• Write the claim again using the opposite symbol:

• Label each statement.

o (null hypothesis):
o (alternative hypothesis):

• Write the Critical value (the Table value) here:

• Now use your calculator or the formula to tell me the calculated value (known as the “test
statistic”):
• REJECT : YES or NO

• What is your conclusion?
• Do the results of the hypothesis test support the results from the confidence interval from
problem #3?

#5 (CH. 9-3) In a study of birth order and intelligence, IQ tests were given to 18 and 19 year
old men to estimate the similarity, if any, between mean IQ’s of firstborn sons and second born sons.

Firstborn: n = 10, mean = 101.5, standard deviation = 13.6
Secondborn: n=10, mean = 102.4, standard deviation = 9.14

Using a 0.05 significance level, test the claim that the average IQ for a FIRSTBORN son is the same as
the average IQ for the SECONDBORN son.

• Write the claim using symbols (< or ≥ or > or ≤ or = or ≠):

• Write the claim again using the opposite symbol:

• Label each statement.

o (null hypothesis):
o (alternative hypothesis):

• Write the Critical value (the Table value) here:

• Now use your calculator or the formula to tell me the calculated value (known as the “test
statistic”):
• REJECT : YES or NO

• What is your conclusion?
#6 (Ch. 9-3) Use the data from problem # 5 and construct a 95% confidence interval. Does the
interval indicate a difference between the results of the two groups?

a. What is the calculated Confidence Interval:

b. Does the interval show there is a difference between the two groups?

c. Do the results of the hypothesis test in problem #5 support the results from this confidence
interval calculation?
#7 (CH. 9-4) A study was conducted to investigate some effects of physical training. Sample
data are listed below with all weights given in kilograms. Using a 0.05 significance level, test the
claim that there is a difference between the pretraining and posttraining weights.

NOTE: if you are not using the calculator shortcut, the easiest way to do this problem is to first
find the “DIFFERENCE” for each set. This becomes your new data set. THEN find the MEAN and STANDARD
deviation of those values. So is and is the standard deviation (also known as from the TI-
calculator shortcut ). Then plug these into the formula to find the Test Statistic.

PRETRAINING WT. 99 57 62 68 72 77 59 91 70 85
POSTTRAINING WT. 91 67 62 69 66 79 58 99 70 84

•

•

• Write the claim using symbols (< or ≥ or > or ≤ or = or ≠):

• Label each statement.

o (null hypothesis):
o (alternative hypothesis):

• Write the Critical value (the Table value) here:
• Now use your calculator or the formula to tell me the calculated value (known as the “test
statistic”):
• REJECT : YES or NO

• What is your conclusion?
#8 (CH. 9-4) Use the data from problem #7 to construct a 95% confidence interval estimate for the
mean of the differences. Does this interval contain zero? Do the results of this problem support the
results of problem #6?
• What is the Confidence Interval Estimate:

• Does the interval indicate a difference or not? Explain your answer.
• Do the results of the hypothesis test (from problem #7) and the confidence interval estimate
support each other?
1) (CH. 7.2) The results of a class experiment showed that out of 2010 M&M’s, 306 were red. Using
this information, I would like for you to construct a 99% confidence interval estimate for the true
percentage of red M&M’s.

• What is the critical Z value:

• What is the confidence interval (round to nearest whole number %):
1b) M&M/Mars claims that 13% of the batch should be red m&m’s. If you rounded your confidence
interval estimate numbers to the nearest whole number percentage, would this survey data support that
claim?
• Conclusion:

2a) (CH. 7.2) An internet service provider sampled 540 customers and found that 75 of them
experienced an interruption in high-speed service during the previous month. Construct a 90%
confidence interval estimate for the proportion of all customers who experienced an interruption.
• What is the critical Z value:

• What is the confidence interval (round to nearest whole number %):

2b) The company’s quality control manager claims that no more than 10% of its customers experienced
an interruption during the previous during the previous month. Does the confidence interval contradict
this claim? Explain your answer.

3) An educator wants to construct a 90% confidence interval for the proportion of elementary
school children in Ohio who are proficient in reading. Estimate the sample size needed to conduct this
survey and assume that there is no information available to be used for an estimate of . Use a
margin of error of 4%.

• What is the critical Z value:
• What is the sample size ?
4a) (CH. 7.3) A sample of 30 quarters was taken and it was found that the average weight was 5.522
g with a standard deviation of 0.058 g. Based on this random sample, construct a 95% confidence
interval estimate of the population MEAN of all quarters in circulation. (Assume that the population
standard deviation is unknown.) Round your final calculation to three decimal places.
• What is the critical T value:

• What is the confidence interval:

4b) The U.S. Department of Treasury claims that it mints quarters to yield a mean weight of 5.670
g. Is this claim consistent with the confidence interval you just calculated? Explain your conclusion
and account for any possible discrepancies.
• Conclusion:

5) (CH. 7.3) Boxes of cereal are labeled as containing 14 ounces. Construct a 95% confidence
interval estimate for the mean weight. (Assume a normal distribution and that the population standard
deviation is unknown.)

14.2 14.1 14.2
14.0 13.9 14.0
13.9 14.3 13.8
13.7 13.9 13.9
• What is the calculated mean (round to 1 decimal place):

• What is the calculated standard deviation (round to 2 decimal places):

• What is the critical T value?

• What is the confidence interval (round each value to 2 decimal places):
• The quality control manager is concerned that the mean weight is actually less than 14 ounces.
Based on the confidence interval, is there a reason to be concerned? Explain your answer.
6) (CH.8.3) A major newspaper ran a report about a poll that was conducted in the southern United
States concerning Elvis. Out of the 1918 adults surveyed, 11% of them believed that Elvis Presley was
still alive. The article began with the claim that “10% of Southerners still think Elvis is alive”.
Using a 0.05 significance level, test the claim that the true population percentage of believers is
greater than 10%.

• Write the claim using one of the following symbols (< or ≥ or > or ≤ or = or ≠):

• Write the claim again using the opposite symbol:

• Label each statement. The one with EQUALITY gets the :

o (null hypothesis):
o (alternative hypothesis):
• Write down the value given for the significance level:

• Write the Critical value (the Table value) here:
• Now use your calculator or the formula to tell me the calculated value (known as the “test
statistic”):
• REJECT : YES or NO

• What is your conclusion?

7) (CH. 8.3) The results from a 2010 survey conducted by a recruiting firm showed that 60% of U.S.
companies use social networks such as Facebook and LinkedIn to recruit job candidates. An economist
thinks that the percentage is higher at technology companies. She samples 180 technology companies and
finds that 116 of them use social networks. Use a 0.01 significance level to test the claim that more
than 60% of technology companies use social networks to recruit job candidates.

• Write the claim using one of the following symbols (< or ≥ or > or ≤ or = or ≠):

• Write the claim again using the opposite symbol:

• Label each statement. The one with EQUALITY gets the :

o (null hypothesis):
o (alternative hypothesis):
• Write down the value given for the significance level:

• Write the Critical value (the Table value) here:
• Now use your calculator or the formula to tell me the calculated value (known as the “test
statistic”):
• REJECT : YES or NO

• What is your conclusion?