Homework

1
Homework

• Worksheet 2
• Confidence Intervals of Means

2
1. Group of 12 has mean annual profit revenue
of 4.4 with st. dev. 1.6 while the mean annual
profit for 10 health care companies was 4.6 with
st. dev. of 1.4. Find 90 interval. Does the
ins. Industry group have a higher mean than the
health care group.
µ1 Mean of revenue for the insurance industry
group µ2 Mean of revenue for the health care
group µ1-µ2 Mean difference in of revenue for
the two groups
Df9
Assumptions 1. Randomly Selected samples
2. Approx. Norm (Pop) use t-dist since s1
and s2are unknown. 3. At least 120
industry people and 100 health care workers
Im 90 confidence that the mean difference
between insurance industry health care is
between (-1.37 and 0.97). Furthermore, since the
interval contains zero, there is no significant
difference between the mean annual revenue for
the insurance industry and health care companies.
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2. Mean height of 45 pro football players is
6.18 with st. dev. 0.37 while 40 pro basketball
players was 6.45 with st. dev. Of 0.31. Find 95
int for difference in mean heights. Are football
players shorter?
µ1 Mean height of pro football players µ2
Mean height of pro basketball players µ1-µ2 Mean
difference in mean height of pro football
basketball players
Assumptions 1. Randomly Selected Samples
2. SD is approx. normal since n1gt30 and n2 gt
30. 3. Independent.
use t-dist since s1 and s2are unknown
Im 95 confidence that the mean difference
between the heights of pro football and
basketball players is between 0.42 and 0.12 ft.
Furthermore, since the entire interval is
negative, the mean height of foot ball players is
between 0.42 and 0.12 ft less than basketball
players.
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3. Claims the average salary is 29,800. The
union claims it is less. They take a sample of
64 employees and find their average salary is
29,000 with st. dev of 800. Use a 5 level of
significance.
.
µ Mean salary of the workers at the Fleetfoot
Shoe Company.

• Assumptions
• SRS
• Approx. Normal since ngt30

Use t-dist since s is unknown
Reject the Ho since P-value (0)lta (0.05). There
is sufficient evidence to support the claim that
the mean salary is less than 29,800
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4. Sample of 43 eastern colleges had avg.
salary increase of 3.6 with st. dev. 1.8 while
40 western colleges had a men increase of 3.3
with st. dev. Of 1.7. Find 90 int. Is the
increase for eastern colleges higher than for
western colleges.
µ1 Mean salary increase for eastern
colleges µ2 Mean salary increase for western
colleges µ1-µ2 Mean difference in mean salary
increases for eastern western colleges
Assumptions 1. Randomly selected samples
2. SD is approx. normal since n1gt30 and n2 gt
30. 3. Independent.
use t-dist since s1 and s2are unknown
Im 90 confidence that the mean difference
between the salary increase for eastern
western colleges is between -.35 and 0.95.
Furthermore, since interval contains zero, there
is no significant difference in the mean salary
increase for eastern and western colleges.
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5. Sample of 18 male wolves from Canada had avg.
weight of 98 lb with st. dev. of 6. 5 lb, while a
group of 24 from Alaska had an avg weight of 90
lb with st. dev. of 7.3 lb. Find 95 interval.
Are Canadian wolves larger?
µ1 Mean weight of Canadian wolves µ2 Mean
weight of Alaskan wolves µ1-µ2 Mean difference
in mean weight of Canadian Alaskan wolves
Assumptions 1. Randomly selected samples
2. pop is approx. norm, but use t dist since
n1lt30 and n2 lt30. 3.
Independent..
Im 95 confidence that the mean difference
between the mean weight of Canadian wolves and
Alaskan wolves is between (4.78 and 11.22) lb.
Furthermore, since the entire interval is
positive, the Canadian wolves are between 4.78 lb
and 11.22 lb heavier.
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6. The average children in 14 low income
families was 4.857 with a st. dev. Of 2.77 while
the average children in 16 high income families
was 4.1875 with a st. dev. Of 2.48. Is there a
difference.
µ1 Mean children in low income familes µ2
Mean children in high income families µ1-µ2
Mean difference in mean children in low and
high income families
Assumptions 1. Randomly selected samples
2. Approx. Norm (boxplts somewhat
symmetrical) but use t-dist since n1lt30 and n2
lt 30. 3. Independent.
Im 95 confidence that the mean difference
between the mean number of children is between
(-1.42 and 2.75). Furthermore, since interval
contains zero, there is no significant difference
in the mean number of children of low and high
income families.
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7. The average score for the 30 in the control
group was 349.2 with st. dev. Of 56.6 while the
30 in the experiemental group had an average of
368.4 with st. dev of 39.5. Use 1 significance
level.
.

• Assumptions
• Randomly selected samples
• Approx. Normal since n1gt30 and n2gt30
• 3. Indepentdent

µ1 Mean score for control group µ2 Mean
score for experimental group µ1-µ2 Mean
difference in score
use t-dist since s1 and s2are unknown
Fail toReject the Ho since P-value (.064)lta
(0.01). There is insufficient evidence to support
the claim that the mean score for the
experimental group was better than the control
group.
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8. A group of 15 patients had an average stay of
7.29 days with a st. dev.of 0.795 days. Find a
99 interval for the mean number of days the
patients spend in the hospital.
µmean number of days the patient spends in the
hospital
Assumptions 1. SRS 2. Pop is
approx. norm but use t-dist since nlt30 Also
boxplot is somewhat symetrical.
Im 99 confidence that the mean number of days
the patients spends in the hospital is between
6.68 days and 7.9 days.