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problem 1)a) prepare down general procedure for testing of hypothesis. Describe each and every step.    

b) A grocery store has specially packaged oranges and has claimed bag of oranges will yield 2.5 quarts of juice. After randomly selecting 42 bags, a stocker found the average juice production per bag to be 2.2 quarts. Historically, we know the population standard deviation is 0.2 quart. Using this sample and a decision criterion of 2.5 standard errors, could we conclude the store’s claims are correct?   

problem 2)a) Under what condition is it suitable to use a one-tailed test? A two-tailed test?

b) Your null hypothesis is that battery for a heart pacemaker has an average life of 300 days, with the alternative hypothesis being that the battery life is more than 300 days, you are the quality control engineer for the battery manufacturer.   

c) What is the relationship between the significance level of a test and type I error?

problem 3)a)    Intel, a manufacturer of chips for computers, is in a process of deciding whether to replace its current semi automated assembly line with fully automated assembly line. Intel has gathered some preliminary test data about hourly production, which is summarized in the following table, and it would like to know whether it should upgrade its assembly line. State (and test at) suitable hypotheses to help Intel decide.
                                 x‾          s       n
Semiautomatic line    198          32    150
Automatic line           206         29    200

b) Service tires at present produce tires at their Karachi plant during two 12-hurs shifts. The night-shift employees are planning to ask for raise as they believe they are producing more tires per shift than the day shift. “Because Service is making more money during night shift, those employee must also make more money” according to night-shift spokesman. Javaid Aslam, the Service production super-visor, randomly selected some daily production runs from each shift with the results given below (in 1,000s of tires produced)   
Shift    Production (in 1,000s)

Day      107.5    118.6    124.6    1016    113.6    119.6    120.6    109.6    105.9
Night    115.6    109.4    121.6    128.7    136.6    125.6    121.3    180.6    117.5

Do these data indicate, at that the night shift is producing more tires per shift?

c) A group of clinical physicians is performing tests on patients to find out the effectiveness of new antihypertensive drug. Patients with high blood pressure were randomly chosen and then randomly assigned to either the treatment groups (which received a well-established antihypertensive) ore percentage of patients whose blood pressure as reduced to a normal level with 1 year. At the 0.01 level significance, test suitable hypotheses older drug in reducing high blood pressure.

Groups        Proportion That Improved    Number of Patients
Treatment                 0.45                             120
Control                     0.36                             150

problem 4)a)    Sales of major appliances differ with new housing marked: when new home sales are good, so are the sales of dishwashers, washing machines, drier, and refrigerators. A trade association compiled the following historical data (in thousands of units) on major appliance sales and housing starts:

Housing Starts (thousands)    Appliance Sales (thousands)
2.0                                                  5.0
2.5                                                  5.5
3.2                                                  6.0
3.6                                                  7.0
3.3                                                  7.2
4.0                                                  7.7
1.2                                                  8.4
4.6                                                  9.0
4.8                                                  9.7
5.0                                                 10.0

i) Develop the equation for the relationship between appliance sales (in thousands) and housing starts (in thousands).

ii) Interpret slope of the regression line.

iii) find out and interpret standard error of estimate.

b) Bank is interested in reducing amount of time people spend waiting to see personal banker. The bank is interested in the relationship between waiting time (Y) in minutes and number of bankers on duty (X). Customers were randomly selected with the data given below:

X      2         3       5       4       2       6      1        3        4       3        3       2        4
Y    11.8    11.3    3.2    6.4    11.    3.2    8.7    10.5    8.2    11.3    9.4    12.8    8.2

problem 5)a) Mr. Ajmal owns corner fruit stand in small town. After hearing many complaints that his prices constantly changes during summer, he has decided to see whether this is true. Based on following data, help Mr. Ajmal compute the suitable weighted aggregate price indices for each month. Use June as the base period. Is your result a Laspeyres index or a Paasche index?
Fruit    Price per Pound    No. of Pounds Sold

                       June    July        Aug.    June
Apples            $0.59    $0.64    $2.00    900
Oranges            0.75    0.65     0.70     200
Peaches             0.87    0.90     0.85    125
Watermelons      1.00    1.10    0.95    350
Cantaloupes       0.95    0.89    0.90    150

b) In preparation for appropriation hearing, police commissioner of a Gujranwala has collected the following information:

Type of Crime        1992    1993    1994     1995
Assault and rape    110       128      134     129
Murder                   30         45       40       48
Robbery                640       720      770      830
Larceny                2,450    2,630    2,910    2,890

Compute unweighted average of relative quantity index for each of these years using 1995 as the base period.

Statistics and Probability, Statistics

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