# d Draw the bar graph associated with c above

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```							                          62.172 Intro to Statistical Inference
Review for Midterm 1

1. Continue Question 4 in homework 2
(b) Find the marginal frequencies
(c) Find the conditional distribution by faculty
(d) Draw the bar graph associated with (c) above.
(e) Find the percentage of Science students who have brown eyes.

2. A recent graduate moving to a new job collected a sample of monthly rent (dollars)
and size (sq ft) of 2-bedroom apartments in one area of a Midwest city.

Size       900       925        932       940       1000       1033      1050       1100
Rent       550       575        620       620        650        675       715        840

(a) Plot the scatter diagram and find the least square line of fit (regression line).
(b) Do these data substantiate the claim that the monthly rent increases with the size
of the apartment? (Test at 5%).
(c) You are looking to rent an apartment with 1025 square feet in that area. Give a
95% confidence interval for the monthly rent of your apartment.

3. Applicants for public assistance are allowed an appeals process when they feel unfairly
treated. At such a hearing, the applicant may choose self-representation or representation
by an attorney. The appeal may result in an increase, decrease, or no change of the aid
recommendation, Court record of 320 appeals cases provided the following data

Amount of Aid
Increased              Unchanged              Decreased
Self-represented               59                    108                     17

Attorney                   70                      63                       3

Test at the 5% level of significance to see whether the appeals decision and the type of
representation are dependent.

4. A shipment of assorted nuts is labeled as having 45% walnuts, 20% hazelnuts, 20%
almonds, and the rest pistachios. By randomly picking several scoops of nuts from this
shipment, an inspector finds the following counts:

Walnuts      Hazelnuts       Almonds         Pistachios
Counts       95            70             33                42

At the 2.5% level, could these findings be a strong basis for an accusation of mislabeling?

5. Four fabrics are tested for flammability at the National Bureau of Standards. The
following burn times in seconds are recorded after a paper tab is ignited on the hem of a
Fabric 1                Fabric 2          Fabric 3            Fabric 4
17.8                    11.2              11.8                14.9
16.2                    11.4              11.0                10.8
17.5                    15.8              10.0                12.8
17.4                    10.0               9.2                10.7
15.0                    10.4               9.2                10.7

(a) At 10%, can we say that fabric 2 and 4 have different variances?

(b) At 5%, are there differences in the mean degree of flammability of the four
fabrics?

Education              Science          Arts          Music
Brown eyes     84                    91             135          112         .87
Blue eyes      17                    25              12           7          .13
.21                   .24             .30          .25       N = 483

(c)
Education              Science          Arts          Music
Brown eyes    .83                   .78             .92          .94         422
Blue eyes     .17                   .22             .08          .06          61
101                   116              147          119       N = 483

(d)
Bar Graph of Faculties by eye colour

1

0.8
Percent

0.6                                                           Series1
0.4                                                           Series2

0.2

0
1              2             3               4
Faculty

1 = Educ; 2 = Sci; 3 = Arts; 4 = Music                    Series 1 = Brown eyes; Series 2 = blue eyes

(e) P(brown / Sci) = 78.45%

2. (a) regression line:         y = 1.2126x – 538.786
(b) t = 7.41, Reject H0; yes.
(c) (622.4, 785.8)

3. chi square = 15.73; Reject H0; yes, they are dependent.

4. chi square = 17.34; Reject H0; yes.

5. (a) F = 1.57, Accept H0; not enough evidence to prove a difference.
(b) F = 13.89, Reject H0; at least 2 fabrics have different degree of flammability.

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