(1 point) The following data represents a random sample of birth weignts (in kgs
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Question
(1 point) The following data represents a random sample of birth weignts (in kgs) of male babies born to mothers on a special vitamin supplement. 3.73 3.02 4.37 4.09 3.73 2.47 4.33 4.13 3.39 4.47 3.68 3.22 4.68 3.43 (a) Do the data follow a normal distribution Report the P-value of the normality test: + (b) Do the data support the claim that the mean birth weight of male babies that have been subjected to the vitamin supplement is at least 3.39 kgs? Use the p-value approach, and regulate the probability of committing Type I error to 5% (-0.05) The p-value is: Does this support the claim+ Use three decimalsExplanation / Answer
we shall perform the analysis in R as shown below
data <- c(3.73,3.02,4.37,4.09,3.73,2.47,4.33,4.13,3.39,4.47,3.68,3.22,4.68,3.43)
## shapiro test for normality
shapiro.test(data)
## test for atleast 3.39 kgs
t.test(data,mu=3.39,alternative = "greater")
The results are
shapiro.test(data)
Shapiro-Wilk normality test
data: data
W = 0.96753, p-value = 0.842 , as the p value is not less than 0.05 , hence we conclude that the data comes from normal distribution
t.test(data,mu=3.39,alternative = "greater")
One Sample t-test
data: data
t = 2.2641, df = 13, p-value = 0.02066 , as the p value is less than 0.05 , hence we reject the null hypothesis in favor of alternate hypothesis and conclude that the claim is supported
alternative hypothesis: true mean is greater than 3.39
95 percent confidence interval:
3.472153 Inf
sample estimates:
mean of x
3.767143
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