Question

Below are the cash receipts in dollars for ice cream vendors at two locations at a city beach: 6.10 North 290.15 183.75 205.35 193.86 256.89 201.15 207.99 299.23 235.18 South 188.86 202.45 215.35 180.77 200.45 205.65 157.84 295.46 201.35 Assuming the differences of daily receipts are independent, test the hypothesis that cash receipts for the north location are usually greater than for the south location against the null hypothesis that the median difference is 0. Use the sign test at the a- 0.10 level of significance. Follow Example 6.6. Do women recover their weight after childbirth? Below Weight gains. are the weights in pounds of a random sample of 20 women measured during an office visit when a pregnancy was first diagnosed. Ten years later, the same women were weighed again. This sample was taken from a population of 1296 women who were part of the Kaiser Foundation Health Plan during the period 1961-1972.4 Example 6.6 Subject: 1 2 3 4 5 6 7 8 9 10 Before: 112 119 130 115 151 137 162 116 130 121 After: 125 130 139 132 155 146 167 130 153 118 Subject: 11 12 13 14 15 16 17 18 19 20 Before: 112 140 136 129 115 102 138 133 118 185 After: 112 157 155 136 136 111 175 172 121 163 Test whether women gain weight in the 10 years after a pregnancy at the α 5% level of significance Solution Here we use the sign test, listing the six steps mentioned in the box above. Let π be the proportion of women in the population of N-|296 who increase in weight over the 10-year period. Step 1·Ho : The median weight has remained the same (π-0.5). Step 2. Ha : The median weight has increased (n > 0.5) Step 3. a 0.05 Step 4. Because there is one tie, which is discarded, it leaves us with a sample of n 19. There are 17 increases in weight, so 17 signs (+) and 2 signs (-). The test statistic is ks 17. Step 5, The P-value is calculated using the π-0.5 column of Table 2 for the group n 19 on page 507. P-value Pr(K k)1-0.9996- 0.0004. Because P-value

Answer 1

step 1)

Ho: median difference(North-South) = 0

step 2)

H1: median difference>0

step 3)

α=0.10

step 4)

there is total 6 positive signs , 3 negative, total n = 9 ,

test statistic = 6

step 5)

p value for n=9,p=0.05, k=6

P value =P(K≥6) = 1-0.7461=0.2539

since, p value>α=0.10, fail to reject Ho

step 6)

The conclusion: there is not enough evidence to conclude that cash receipts for North are usually larger than South location at α=0.10