Discuss the below:
Q1. Past experience indicates that the time required for high school seniors to complete a standardized test is a normal random variable with a standard deviation of 6 minutes. Test the hypothesis that o = 6 against the alternative that o < 6 if a random sample of 20 high school seniors has a standard deviations s = 4.51. Use a 0.05 level of significance.
Q2. Past date indicate that the amount of money contributed by the working residents of a large city to a volunteer rescue squad is a normal random variable with a standard deviation of $1.40. It has been suggested that the contributions to the rescue squad from just the employees of the sanitation department are much more variable. If the contributions of a random sample of 12 employees from the sanitation department had a standard deviation of $1.75, can we conclude at the 0.01 level of significance that the standard deviation of the contributions of all sanitation workers is greater than that of all workers living in this city?
Q3. Two types of instruments for measuring the amount of sulfur monoxide in the atmosphere are being compared in an air-pollution experiment. It is desired to determine whether the two types of instruments yield measurements having the same variability. The following readings were recorded for the two instruments:
Sulfur Monoxide
|
Instrument A
|
Instrument B
|
|
0.86
|
0.87
|
|
0.82
|
0.74
|
|
0.75
|
0.63
|
|
0.61
|
0.55
|
Sulfur Monoxide
|
Instrument A
|
Instrument B
|
|
0.89
|
0.76
|
|
0.64
|
0.70
|
|
0.81
|
0.69
|
|
0.68
|
0.57
|
|
0.65
|
0.53
|
Assuming the populations of measurements to be approximately normally distributed, test the hypothesis that oA does not equal oB. Use a P-value.