Starting in the 1970s, medical technology allowed babies with very low birth wei

Question

Starting in the 1970s, medical technology allowed babies with very low birth weight (VLBW, less than 1500 grams, about 3.3 pounds) to survive without major handicaps. It was noticed that these children nonetheless had difficulties in school and as adults. A long-term study has followed 245 VLBW babies to age 20 years, along with a control group of 223 babies from the same population who had normal birth weight.

IQ scores were available for 118 women in the VLBW group. The mean IQ was 83.9, and the standard deviation was 12.7. The 133 women in the control group had mean IQ 87.2, with standard deviation 12.4.

The test statistic for the a null hypothesis of "no difference" question using the VLBW women as group 1 is ____. (±0.001)

Is this difference between the two groups statistically significant at =0.005?

Yes

No

Explanation / Answer

Solution:

Here, we have to use two sample t test assuming equal population variance.

The null and alternative hypothesis is given as below:

Null hypothesis: H0: There is no any statistically significant difference in the average IQ score of the women in VLBW group and control group.

Alternative hypothesis: Ha: There is a statistically significant difference in the average IQ score of the women in VLBW group and control group.

H0: µ1 = µ2 versus Ha: µ1 µ2

This is a two tailed test.

Test statistic formula for pooled variance t test is given as below:

t = (X1bar – X2bar) / sqrt[Sp2*((1/n1)+(1/n2))]

Where Sp2 is pooled variance

Sp2 = [(n1 – 1)*S1^2 + (n2 – 1)*S2^2]/(n1 + n2 – 2)

We are given

X1bar = 83.9

X2bar = 87.2

S1 = 12.7

S2 = 12.4

n1 = 118

n2 = 133

df = 118 + 133 – 2 = 249

= 0.005

Lower critical value = -2.8323

Upper critical value = 2.8323

(By using t-table)

Sp2 = [(118 – 1)*12.7^2 + (133 – 1)*12.4^2]/(118 + 133 – 2)

Sp2 = 157.2982

(X1bar – X2bar) = 83.9 - 87.2 = -3.3000

t = -3.3 / sqrt(157.2982*((1/118)+(1/133)))

t = -2.0806

The test statistic for the a null hypothesis of "no difference" question using the VLBW women as group 1 is t = -2.0806.

P-value = 0.0385

P-value > = 0.005

So, we do not reject the null hypothesis that there is no any statistically significant difference in the average IQ score of the women in VLBW group and control group.

There is insufficient evidence to conclude that there is a statistically significant difference in the average IQ score of the women in VLBW group and control group.

Is this difference between the two groups statistically significant at =0.005?

No

(Because, P-value > = 0.005)

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