# Stat 160 postquiz over sections 8.1, 8.2, 8.3, and 8.4

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1.     We are interested in comparing the batting averages of baseball players; specifically the batting averages of the right-handed hitters and the left-handed hitters. We decide to take a sample of 15 right-handed and 8 left-handed hitters. Let T be the number of times a batting average of a left-handed hitter is bigger than the batting average of a right-handed hitter. Under the null hypothesis, i.e. assuming there is no difference in the averages of right- and left-handed hitters, what do you expect T to be?

22
11
120
60
2.     Below are the actual batting averages of the right-handed hitters and the left-handed hitters discussed in #1. Compute the value of T .
Right .225    .238    .239    .243    .244    .245    .262    .271
.271    .274    .274    .276    .282    .286    .286

Left  .238    .271    .279    .283    .284    .290    .300    .303

113
91
92.5
60
3.     Refer to the situation in problems 1 and 2 above. Suppose we want to test
• H0 : The batting averages of right-handed and left-handed hitters are the same
• HA : The batting averages of right-handed and left-handed hitters are not the same
• Using the class code  Wilcoxon1 , 100 trials were performed (computing T in the manner described in problem 1). The following are sorted Wilcoxon statistic values. What is the p-value?
18.0  27.0    30.0    32.5    32.5    35.0    35.0    35.5    38.0    38.5
39.0  39.5    42.0    42.5    43.0    43.5    44.5    45.5    48.0    48.5
49.5  49.5    49.5    50.0    50.0    51.0    51.5    52.0    52.5    52.5
53.0  53.5    55.0    55.5    56.5    57.0    57.5    57.5    57.5    58.0
58.0  58.0    58.0    58.5    59.0    59.0    59.5    59.5    60.0    61.0
61.0  62.0    62.5    62.5    63.0    65.0    65.0    67.5    67.5    67.5
68.0  68.0    69.0    70.5    70.5    71.5    72.0    73.0    73.5    73.5
74.0  74.0    74.5    74.5    74.5    75.0    75.0    76.5    76.5    77.0
77.5  77.5    77.5    78.0    78.5    78.5    79.5    81.5    82.5    83.5
86.0  86.0    86.5    87.0    88.5    89.0    89.5    93.5    97.0    99.5

.52
.06
0
.60
4. During morning rushhour, are all lanes of a 5-lane expressway into Houston used at the same level; that is, are all lanes used uniformly? Here are the counts of cars in a minute interval of the rushhour during one work day:
200 225 350 320 380

Suppose the lanes are used at the same level (a car is equilikely to be in any of the 5 lanes), how many would you expect in each lane for this minute interval?

0
1475
295
320
5. What is the value of the chi-squared goodness of fit test statistic for the data in Problem 4.

Accept Ho
84.1
295
1.96