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## Statistics

problem 1) A school wishes to estimate average weight of students in the 6th grade. Standard deviation of population is known to be 15 lbs. Random sample of 8 values is chosen; the values in lbs are 8.5, 9.6, 10.7, 10.9, 11.5, 11.6, 12.8 and 9.3. find out the 90% and 95% confidence interval for the population mean.

b) Examination was given to two groups of 40 female and 50 male students, respectively. Female mean grade was 74 and S.D. of 8, while male mean grade was 76 with S.D. of 7. Determine the 95% confidence interval for the difference in population mean grade between male and female students i.e.

problem 2)a) To estimate average weekly income of unskilled workers in a large city the investigator collected weekly income data from a random sample of 25 unskilled workers. Sample mean and S.D. are found to be Rs. 927 and Rs. 15 respectively. Test hypothesis that average income (weekly) of the workers is less than Rs. 1025. Use 5% level of significance.

b) Metro discount store has always prided itself on customer service. Store hopes that all metro stores are providing the same level of service from coast to coast, so they have surveyed some customers. In the Karachi region, a random sample of 97 customers yielded an average overall satisfaction rating of 8.8 out of 10 and the sample standard deviation was 0.7. In the Lahore region, a random sample of 84 customers resulted in an average rating of 9.0 and the sample standard deviation was 0.6. Can Metro conclude, at α = 0.05, that the levels of customer satisfaction in the two markets are significantly different?

problem 3)a) State and describe Statistical Process Control. Define various control charts.

b) quality control effort is being attempted for a process where large steel plates are being manufactured and surface defects are of concern.

The goal is to set up a quality control chart for the number of defects per plate. The data are as follows:

Sample Plate    Number of Defects     Sample Plate    Number of Defects
1                                 4                         11                1
2                                 2                         12                2
3                                 1                         13                2
4                                3                          14                3
5                                0                          15                1
6                                4                          16                4
7                                5                          17                3
8                                3                          18                2
9                                2                          19                1
10                              2                          20                3

Set up the appropriate control chart, using this sample information. Does the process appear to be in control?

problem 4)a) The following table shows the likings of three colors pink, white and blue in a sample of 200 males and females.

Colors             Sex
Males    Females
Pink        20         40
White     40         20
Blue       60         20

Test whether is there any relation between sex and color. Use α = 0.05.

b) Fauji Fertilizer Company is making fertilizer of three types. Yield of wheat (in kg/acre) after using each fertilizer (5 kg) during last 6 years as follow:

Urea                   52    57    59    54    58    59
Phosphorus        42    45    49    41    43    45
Nitrogen             79    78    77    74    73    76

Using ANOVA technique, Is there any major difference in these fertilizers?

problem 5) Sprite soft drink Company is studying the effect of its latest advertising campaign. People chosen at random were called and asked how many cans of Sprite they had bought in the past week and how many Sprite advertisement they had either read or seen in the past week.

X (number of ads)      3      7      4    2    0    4    1    2
Y (Cans purchased)    11    18    9    4    7    6    3    8

i) Fit and interpret the equation Y = a + bX

ii) Also test the regression coefficient i.e., b = 0

Statistics and Probability, Statistics

• Category:- Statistics and Probability
• Reference No.:- M95997

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