Question

1. During a particular week, 60 babies were born in a maternity unit. Part of the standard procedure is to measure the length of the baby (in centimeters). The sample of 60 babies gives a sample mean of 48.33 and sample standard deviation of 4.16. Is there evidence that the true length of babies is less than 50 centimeters?

Answer 1

Here, we have to use one sample t test for the population mean.

The null and alternative hypotheses are given as below:

H₀: µ = 50 versus H_a: µ < 50

This is a lower tailed test.

The test statistic formula is given as below:

t = (Xbar - µ)/[S/sqrt(n)]

From given data, we have

µ = 50

Xbar = 48.33

S = 4.16

n = 60

df = n – 1 = 59

Assume α = 0.05

Critical value = -1.6711

(by using t-table or excel)

t = (Xbar - µ)/[S/sqrt(n)]

t = (48.33 - 50)/[4.16/sqrt(60)]

t = -3.1096

P-value = 0.0014

(by using t-table)

P-value < α = 0.05

So, we reject the null hypothesis

There is sufficient evidence to conclude that the true length of babies is less than 50 centimeters.