Statistics -Hypothesis Testing

2013-05-13 2:07 am

Question 3 [8 marks]
The proportion of babies with a low birth weight is an indicator of nutrition for the mothers.For a large city, a researcher claimed that at least 7% of babies have a low birth weight. To check this claim, a random sample was taken, and 23 babies out of a random sample of 209 babies have a low birth weight. At a significance level of 0.05, is there any evidence to support the researcher’s claim?

Question 4 [7 marks]
Assume that the weight of cereal in a “10-ounce box” is normally distributed.
To test H0: μ≤ 10.1 against H1: μ> 10.1, we take a random sample of size n=16 and observe that the mean is 10.4 and standard deviation is 0.4. Do we reject H0 at the 5% significance level?

回答 (1)

myisland8132

2013-05-14 4:34 am

✔ 最佳答案

3 H_0 : At least 7% of babies have a low birth weight
H1 : Reject H_0α = 0.05, Z_(1-α) = 1.645, p = 23/209 = 0.110047847√[p_0(1 - p_0)/n] = √[0.07(0.93)/209] = 0.01765Test Statistic = (p - p_0)/[√[p_0(1 - p_0)/n] = 2.269Since 2.269 > 1.645, reject H_0 and conclude that at least 7% of babies have a low birth weight

4 H0:μ ≤ 10.1
H1: μ > 10.1α = 0.05, t_(0.05,15) = 1.753. x = 10.4,s = 0.4Test Statistic = (x - μ)/(s/√n) = (10.4 - 10.1)/(0.4/√16) = 3Since 3 > 1.753, we reject H_0 at the 5% significance level

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