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In a study of the effect of aluminum intake on the mental development of infants, a group of 92 infants who had been born prematurely were given a special aluminum depleted intravenous-feeding solution. At age 18 months the neurologic development of the infants was measured using the Bayley Mental Development Index (BMDI), the results are summarized below:

n Mean SD
92 97.95 20

a. The BMDI is similar to an IQ score, with 100 being the average in the general population. Assuming all relevant assumptions are met, conduct a hypothesis test to determine if the aluminum depleted intravenous-feeding solution adversely affected the mental development of infants. Be sure to include all the steps for full credit.
b. Calculate a 95% confidence interval for the mean Bayley Mental Development Index for the group of infants in the study. Explain how this confidence interval corresponds to the results you found in part (a).

Sagot :

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Answer:

there is no sufficient evidence to support the claim that aluminum depleted intravenous-feeding solution adversely affected the mental development of infants ;

(93.86, 102.04)

Step-by-step explanation:

μ = 100 ; xbar = 97.95 ; n = 92 ; SD = 20

H0 : μ = 100

H1 : μ < 100

The test statistic :

(xbar - μ) ÷ SD/sqrt(n)

(97.95 - 100) ÷ 20/sqrt(92)

-2.05 ÷ 20/sqrt(92)

Test statistic = - 0.983

The Pvalue :

Using the Pvalue calculator at α = 0.05

Pvalue = 0.1628

Decision region :

Reject the null ; if Pvalue < α

0.1628 > 0.05

Hence, we fail to reject the Null ;

In conclusion, there is no sufficient evidence to support the claim that aluminum depleted intravenous-feeding solution adversely affected the mental development of infants

For the 95% confidence interval :

μ ± margin of error

Margin of Error = Zcritical * SD/sqrt(n)

Zcritical at 95% = 1.96

Margin of Error = 1.96 * 20/sqrt(92) = 4.087

97.95 ± 4.087

Lower boundary = 97.95 - 4.087 = 93.863

Upper boundary = 97.95 + 4.087 = 102.037

(93.86, 102.04)

The result of the confidence interval tells us that, the mean Bayley Mental Development Index for the group of infants in the study is still within the general population average.

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