Problem # 1

In
a number of previous Phase I and II studies of male, non-insulin-dependent
diabetic (NIDDM) patients conducted by Mylitech Biosystems, Inc., the mean body
mass index (BMI) was found to be 28.4. An investigator has 20 male NIDDM
patients enrolled in a new study and wants to know if the BMI from this sample
is consistent with the previous finding. BMI is computed as the ratio of weight
in kilograms to the square of the height in meters. The Excel data file
BMI.xlsx shows the BMI for these 20 males. Conduct a hypothesis test at 1%
level of significance to answer the question.

Patient_no	Height_cm	Weight_kg	BMI
1	178	101.7	32.1
2	170	97.1	33.6
3	191	114.2	31.3
4	179	101.9	31.8
5	182	93.1	28.1
6	177	108.1	34.5
7	184	85	25.1
8	182	89.1	26.9
9	179	95.8	29.9
10	183	97.8	29.2
11	172	77.5	26.2
12	183	102.8	30.7
13	169	81.1	28.4
14	177	102.1	32.6
15	180	112.1	34.6
16	184	89.7	26.5
17	176	86.5	27.90
18	187	101.2	28.90
19	175	99.6	32.50
20	193	104.2	27.90

Consider
the following steps for your hypotheses test.

(i)
Formulate
the hypotheses. (Label the parameter, null hypothesis, alternative hypothesis) [3 pts.]

(ii)
Test statistic. (Name of the test you are
going to use and verify all required conditions for your test; using StatCrunch, produce a boxplot to verify the
normality condition) [7
pts.]

(iii)
Calculation of your proposed test statistic
and p-value. (Both StatCrunch output and manual calculations must be reported.
Note that the answer should be the same in both cases) [4 pts.]

Statcrunch output:

(Load the data file on StatCrunch and
then go to STAT® T statistics® one sample with data.

Modify
other boxes according to the question.)

Manual calculation:

(iv)
Decision and conclusion in the context of the
problem. [2
pts.]

Problem # 2

A company reports that 65% of its employees participate in the company’s stock purchase plan. A random
sample of 70 employees was asked the question, ?Do you participate in the stock purchase plan?? The answers
are shown below.

yes no
no yes
no no
yes yes no yes

no no
yes yes yes no yes
no no
yes

yes yes
no yes
yes no
yes yes no yes

yes yes
yes yes
no no
yes yes yes yes

yes yes
no yes
no yes yes no yes
yes

yes
yes no
yes no yes yes no
yes yes

no no
yes yes yes no yes
no no
yes

Perform the appropriate test of hypothesis to investigate your suspicion that fewer than 65% of the company?s
employees participate in the plan. Use ? = .05.
[ Note that # yes = 44, # no =26, and total n=70]

Consider
the following steps for your hypotheses test.

(i)
Formulate
the hypotheses. (Label the parameter, null hypothesis, alternative hypothesis) [3 pts.]

(ii)
Test statistic. (Name of the test you are
going to use and verify all required conditions for your test using the data.) [5 pts.]

(iii)
Calculation of your proposed test statistic
and p-value. (Both StatCrunch output and manual calculations must be reported.
Note that answer should be the same in both cases.) [4 pts.]

Statcrunch
output:

[Go to StatCrunch and then click on STAT® Proportion statistics® one sample with Summary

Enter # of successes 44

# of Observations 70

Change H₀ : p=.65. Choose H_a carefully.

Click on Compute! ]

Manual
calculation:

(iv)
Decision and conclusion in the context. [2
pts.]