# Need Help: Mid-term Exam; STATISTICS

Need Help: Mid-term Exam; STATISTICS

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Answer all Questions (1 -5)                                                                                                   Total points 50

Q 1.  Identify the sample and population. Also, explain whether the sample is likely to be representative of the population.

1. a) 5 students in a large university with more than 10,000 students were asked whether they exercise at least 30 minutes each day and only 2 said yes.

1. b) 10,000 randomly selected adults in Massachusetts were asked whether they support the ballot question number 2 in the current election and 42% said yes while 58% said no.

Q 2.  A medical research team studied the ages of patients who had strokes caused by stress. The ages of 36 patients who suffered stress strokes were as follows.

29   39   36   41   45   50   57   61   28   50   36   38

50   38   36   47   40   35   58   36   61   40   55   42

61   56   45   44   62   36   38   40   45   27   59   31

Construct a frequency distribution for these ages. Use 6 classes beginning with a lower class limit of 25.

Q 3.  In a survey, 28 voters were asked their ages. The results are shown below. Construct a histogram to represent the data (with 5 classes beginning with a lower class limit of 19.5 and a class width of 10). What is the approximate age at the center?

53  56  38  53  67  65  52  48  37  51  40  61   62 53

66  45  41 35  39 32  43  61  43  69  31  48   59 56

Q 4.   Consumer Reports published an article that listed the returns earned by numerous stock funds in 2005. Total percentage returns for 11 of these funds are shown below, listed in no particular order, and rounded to the nearest whole number.

15        29        21        30        26        33        30        32        38      31      27

1. Calculate the mean, median, and mode for the return data.
2. Calculate the range, variance, and standard deviation.
3. Calculate the z score for the return of 34.
4. Assuming that the distribution of above data is symmetric, find the two limits around the mean where we will find 95% of the observations.
5. Find the data at the 70th percentile
6. Find the 5 number summary of the data.
7. Draw and label the complete boxplot.

Q 5.    A company surveyed 100 of its employees at random regarding their age by gender and found the following result

AGE

< 35 years 35-44 years 45-54 years >54 years
 GENDER

Male

11 15 22 10
Female 8 17 13 4

If an employee is selected at random find the probability that the selected employee is

1. Female
2. Is 35-44 year old.
3. Is male and is 45-54 year old.
4. Is male or is 45-54 year old

If two employees are selected at random what is the probability that both employees are females when the selection is made

1. With replacement
2. Without replacement

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