Part I T/F and Multiple Choice Questions - JustAnswer



Part I T/F and Multiple Choice Questions

1.     False

2.     True

3.     True

4.     True

5.     False

6.     False.

7.     True

8.     C. Presenting two quantitative variables.

9.     C. Mode

10.    A. mean

11.     C. 68%

Part II Short Answers and Computational Questions

1.     Variance is the square of the standard deviation. The symbol used for the poulation standard deviation is [pic], while the sample standard deviation is represented by [pic]. The population variance is given by [pic] and the sample variance is given by [pic].

The unbiased estimator of variance is used because it is equal to, on average, the population variance. Other estimators of variance (such as the sample variance with a denominator of n rather than n-1) have some desirable properties, although they are biased. That is, using the denominator of n generally under estimates the population variance.

2.     Mean = 2, Mode = 2, Median = 2, Midrange = 2

3.     a) Chebyshev’s Theorem states that for any positive k, the proportion of the data that lies within k standard deviations of the mean is at least:

1-(1/k^2) .

So, since the standard deviation s 7.5, The range given is within k=2 standard deviations of the mean, so we know that at least 1- ¼ = 75% of the data falls between these values.

b) The empirical rule states, in part that 95.5% of the data falls within 2 standard deviations of the mean (for the normal distribution). That means that 95.5% of the data falls between 234+/-24 = (210,258)

4.     Find P25 for the following data:   

When the median falls between two numbers (as it does in this case), you average those two numbers to find the median value. The same is true here. In this case, the 25th percentile falls between the third and the fourth data point, so we average those two numbers to get the 25th percentile.

P25=1.5 (See the below table for illustration and further explanation)

|Data Value |Percentage of Data below|

| |(including data point) |

|0 |0.083333333 |

|1 |0.166666667 |

|1 |0.25 |

|2 |0.333333333 |

|2 |0.416666667 |

|2 |0.5 |

|3 |0.583333333 |

|3 |0.666666667 |

|3 |0.75 |

|4 |0.833333333 |

|6 |0.916666667 |

|6 |1 |

5.     

The mean is the midpoint of each class times the frequency divided by the total number of observations.

The sample variance is given by this formula:

[pic], where f is the frequency, and m is the midpoint of each class.

The standard deviation is just the square root of the variance.

These values are

Mean = 6.182

Variance = 24.263

Standard Deviation = 4.926

6.     An aptitude test has a mean of 220 and standard deviation of 10. find the corresponding z score for: a) a test score of 232 b a test score of 212   

7.     

a.

a. SSx: 21.4286

b. SSY: 106.857

c. SSxy: -47.286

d.      r: -0.9882

e.     The slope b1 = -2.207

f.     The y-intercept, b0 = 19.26

g.     The equation of the line of best fit: y=-2.207x+19.26

8. If you’ll post this bar graph, I’ll look at it. I suspect, though, that I know what’s happening. I would bet that if you look at the vertical axis that it doesn’t go all the way down to zero. That is, if the boys took 100 seconds and the girls took 110 seconds, then the bar graph probably starts somewhere about 95. That way the difference looks greater than it is.

If this isn’t it, just go ahead and post a pic of the bar graph, and I’ll have a look at it.

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