Question

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1. Breast-feeding mothers secrete calcium into their milk. Some of the calcium may come from their bones, so mothers may lose bone mineral. Previous research shows that the average percent change in mineral content for breast-feeding mothers is μ--4% with standard devi- ation σ 2.5%. Researchers suspect that mothers who drink at least 8 ounces of milk per day while breastfeeding (milk-drinking mothers) lose less bone mineral. They measured the per cent change in mineral content of the spines of 52 milk-drinking mothers during three months of breastfeeding. The data is contained in the Excel file that accompanies this worksheet. (a) (4 points) Make a histogram of the data (use class sizes of 1.5 or 2) to see that they appear to follow an approximately Normal distribution. (b) (4 points) Consider the question: Do milk-drinking mothers lose less bone mineral than all breast-feeding mothers? State the null and alternative hypotheses in terms of mean percent change μ in mineral content. (c) (2 points) Find the z test statistic. (d) (2 points) What is the P-value for your z? (e) (2 points) What do you conclude about the population of milk-drinking mothers? f) (4 points) Sketch the correct picture of an appropriately labeled distribution that corresponds to your computation in part (d). 54933 6475662272392949169926971922329-59742176_465639 -323-04-242058-6-44 2730615561602351 54335 3520661020502

Answer 1

(a)

Histogram Lower class boundary Upper class boundary Frequency 12 2 10 10 10 10 8.5 5.5 10 5.5 -4 2.5 0.5 2 3.5 2 0.5 2 52 3.5 0.5 Total 5.5 0.5 2.5 -5.5 8.5 Class boundary 1.5 Class width-

From the above histogram, we can say that the data appear to follow approximately normal distribution.

b) Let -true average percent change in mineral content for milk drinking mothers Null hypothesis,-Ho : μ=-4 us. Alternative hypothesis. H. μ >-4. (c) z-test where, n = 55, x = sample mean =-3.4462, s = sample sd = 2.4178, then value of z = 1.6517 (d) p-value = P(Z > 1.2982 Z ~ N(0, 1)) 0.0493. (e) Since p-value < 0.05 so we reject Ho at 5% level of significance and conclude that milk-drinkina mothers lose less bone mineral than all breast feediną mothers = Vn (z + 4)

Summary statisti Mean Standard Error Median Mode Standard Deviation Sample Variance Kurtosis Skewness Range Minimum Maximum Sum Count 3.4462 0.3353 3.6 2.4 2.4178 5.8457 0.4092 0.255 10.5 8.2 179.2 52

(f)

ご。 p-value 1.6517 2 0 3 -2