Before health insurance rules were change effective January 1, 2005, the average

Question

Before health insurance rules were change effective January 1, 2005, the average number of days spent in a hospital by a new mother was 2 days. For a 5% level of significance, do the data in the file indicate that women are now spending less time in the hospital after giving birth than they were prior to 2005. Explain your answer in terms of the p-value for the test.

Patient Length 1 1 2 1 3 1 4 1 5 2 6 2 7 2 8 2 9 1 10 1 11 1 12 1 13 1 14 1 15 1 16 1 17 1 18 1 19 1 20 1 21 1 22 1 23 1 24 1 25 1 26 1 27 1 28 1 29 1 30 1 31 2 32 2 33 2 34 2 35 2 36 2 37 2 38 2 39 2 40 3 41 3 42 1 43 1 44 1

Explanation / Answer

Below are the null and alternate hypothesis

H0: mu >= 2
H1: mu < 2

This is left tailed test.
n = 44
xbar = 1.3864
std. dev. s = 0.5793

Test statistics, z = (xbar - mu)/(s/sqrt(n))
z = (1.3864 - 2)/(0.5793/sqrt(44))
z = -7.0260

p-value = 0.0000

As p-value is less than the significance level of 0.05, we reject the null hypothesis.
There are significant evidence to conclude that average number of days spent in a hospital is less than 2.

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