Statistics in a Modern World 800
Solutions to Practice Exam 4

1. (a) since the entire interval for 2002 is above the interval for 1995
2.  
   1. (iii) because the interval is entirely above .5
   2. (ii) because the interval contains .5
3.  
   1. (iv) because two categorical variables (bald or not, heart attack or not) are involved
   2. (i) because one categorical variable (in favor or not) is involved
   3. (ii) because one measurement variable (hours of sleep) is involved
   4. (iii) two-sample z because one measurement (weight) and one categorical variable (year 1995 or 2003) are involved
4. (b) small p-value means strong evidence of a relationship; the relationship itself is not necessarily strong
5.  
   1. mean of sample proportions is population proportion .1
   2. standard deviation of sample proportions is square root of (.1)(1-.1)/16 = .075
   3. (iv) one tenth of 16 is 1.6, not at least 5 as the rule of thumb for normal approximation requires
6.  
   1. (ii)
   2. (i)
   3. (i)
   4. 3.5 plus or minus 3 times 1.7 divided by square root of 8 = (1.7, 5.3) [3.5 plus or minus 3 standard errors, where a standard error is population standard deviation divided by square root of sample size]
7.  
   1. 180 plus or minus 2 times 40 divided by square root of 100 = (172, 188)
   2. (vi)
8. .10/2 = .05
9.  
   1. (ii) large sample makes it easier to reject the null hypothesis
   2. (i) small sample makes it harder to reject the null hypothesis
10.  
    1. (ii)
    2. (iii)
    3. standard error = square root of (.5)(1-.5)/662 = .019; sample proportion = 225/662 = .58 and z = (.58-.50)/.019 = 4.12
    4. p-value is probability of z greater than 4.12, which is approximately 0
    5. (i) p-value very small means definitely reject the null hypothesis and conclude the alternative is true: a majority of men with a preference want a boy

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