Statistics in a Modern World 800
Solutions to Exam 4

1. (c) Since zero is well-contained within the interval, there is no statistical evidence of a difference.
2. (a) The U.S. interval (41,136) is much higher than the Australia interval (9,36) with no overlap.
3. (a) yes!
4.  
   1. (ii) z test about a mean (null hypothesis says mean IQ of children of women smokers equals 100)
   2. (iv) chi-squared test for a relationship between two categorical variables (conviction or acquittal, and religion)
   3. (iii) two-sample z test (comparing 2 means)
   4. (i) z test about a proportion (null hypothesis says proportion correct equals .25)
5. (c) P-value not small at all indicates no evidence of a relationship
6.  
   1. (ii) approximately the same: both should equal population proportion
   2. (iii) more for teaspoons: more spread for smaller samples
   3. (iii) more normal for Tablespoons: Central Limit Theorem gave this result
7.  
   1. mean of sample means=population mean=3.5
   2. standard deviation of sample means = population s.d. over square root of sample size: 1.7/5=.34
   3. (iii) approximately normal because 25 is large enough (Central Limit Theorem again)
   4. within 1 standard error of mean: 3.5 plus or minus .34 = (3.16,3.84)
8.  
   1. .27 plus or minus 2 times square root of (.27)(1-.27)/294) =.27 plus or minus .05, or (.22,.32)
   2. yes, it's a minority because the above interval is so far below .5.
   3. (i) is the only correct interpretation
9. 2(.04)=.08
10.  
    1. (ii) fail to reject the null hypothesis, even when it is false: small sample leads to small z which leads to large P-value which does not provide evidence to reject
    2. (i) find a difference to be statistically significant when it has little practical significance: large sample leads to large z which leads to small P-value which provides evidence to reject
11.  
    1. (v) null hypothesis: population mean for women = .47
    2. (iv) alternative hypothesis: population mean for women less than .47
    3. (29-47)/(16/10)=-11.25
    4. P-value is approximately zero since the z score is so far below zero
    5. (i) yes: small P-value tells us to reject the null hypothesis and conclude the alternative is true.

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