(d) Test the hypothesis that the duration of effusion is different among breastfed babies than among bottle-fed babies using a nonparametric test. (Use Breastfed - Bottle-Fed. Use a = 0.05.) Find the test statistic. (Round your answer to two decimal places.) Use technology to find the p-value. (Round your answer to four decimal places.) p-value =

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Please answer A and D
 
 
A common symptom of otitis media in young children is the prolonged presence of fluid in the middle ear, known as middle-ear effusion. The presence of fluid may result in temporary hearing loss and interfere with normal learning skills in the first 2 years of life. One hypothesis is that babies who are breastfed for at least 1 month build up some immunity against the effects of the infection and have less prolonged effusion than do bottle-fed babies. A small study of 24 pairs of babies is set up, in which the babies are matched on a one-to-one basis according to age, sex, socioeconomic status, and type of medications taken. One member of the matched pair is a breastfed baby, and the other member is a bottle-fed baby. The outcome variable is the duration of middle-ear effusion after the first episode of otitis media. The results are given in the table below.

Duration of Middle-Ear Effusion in Breastfed and Bottle-Fed Babies

Pair Number Duration of Effusion in
Breastfed Baby (days)
Duration of Effusion in
Bottle-Fed Baby (days)
1 20 19
2 11 36
3 3 6
4 24 181
5 7 6
6 28 32
7 58 224
8 7 7
9 39 56
10 17 77
11 17 185
12 12 30
13 52 40
14 14 15
15 12 22
16 30 27
17 7 8
18 15 28
19 65 78
20 10 11
21 7 8
22 19 17
23 34 29
24 25 19
(a) Suppose we're interested detecting whether there is a significant difference in the duration of effusion depending on whether a baby is breastfed versus if they are bottle-fed. What hypotheses
are being tested here (in days)? (Enter != for as needed.)
Ho
H₁:
xA=0
Check which variable(s) should be in your answer.
(b) Why might a nonparametric test be useful in testing the hypotheses?
O The samples of breastfed babies and bottle-fed babies are dependent, but the only parametric tests that can compare differences between two samples require the assumption that
both samples are independent of one another.
O Both samples of breastfed babies and bottle-fed babies appear to be highly skewed and contain outliers, so an assumption of normality in the underlying distributions is unlikely to
hold.
The differences in duration of effusion for the pairs of breastfed and bottle-fed babies appear to be highly skewed with multiple outliers, so an assumption of normality in the
underlying distribution is unlikely to hold.
O The samples of breastfed babies and bottle-fed babies are independent, but the only parametric tests that can compare differences between two samples require the assumption that
both samples are dependent on one another.
(c) Which nonparametric test should be used here?
Othe Wilcoxon signed-rank test
O the sign test
O the Wilcoxon rank-sum test
(d) Test the hypothesis that the duration of effusion is different among breastfed babies than among bottle-fed babies using a nonparametric test. (Use Breastfed - Bottle-Fed. Use α = 0.05.)
Find the test statistic. (Round your answer to two decimal places.)
TV ✔
T =
Use technology to find the p-value. (Round your answer to four decimal places.)
p-value =
Transcribed Image Text:(a) Suppose we're interested detecting whether there is a significant difference in the duration of effusion depending on whether a baby is breastfed versus if they are bottle-fed. What hypotheses are being tested here (in days)? (Enter != for as needed.) Ho H₁: xA=0 Check which variable(s) should be in your answer. (b) Why might a nonparametric test be useful in testing the hypotheses? O The samples of breastfed babies and bottle-fed babies are dependent, but the only parametric tests that can compare differences between two samples require the assumption that both samples are independent of one another. O Both samples of breastfed babies and bottle-fed babies appear to be highly skewed and contain outliers, so an assumption of normality in the underlying distributions is unlikely to hold. The differences in duration of effusion for the pairs of breastfed and bottle-fed babies appear to be highly skewed with multiple outliers, so an assumption of normality in the underlying distribution is unlikely to hold. O The samples of breastfed babies and bottle-fed babies are independent, but the only parametric tests that can compare differences between two samples require the assumption that both samples are dependent on one another. (c) Which nonparametric test should be used here? Othe Wilcoxon signed-rank test O the sign test O the Wilcoxon rank-sum test (d) Test the hypothesis that the duration of effusion is different among breastfed babies than among bottle-fed babies using a nonparametric test. (Use Breastfed - Bottle-Fed. Use α = 0.05.) Find the test statistic. (Round your answer to two decimal places.) TV ✔ T = Use technology to find the p-value. (Round your answer to four decimal places.) p-value =
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