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The number of births per woman in China is 1.6down from 5.91in 1966. This fertility rate has been attributed to the law passed in 1979restricting births to one per woman. Suppose that a group of students studied whether or not the standard deviation of births per woman was greater than 0.75. They asked 50women across China the number of births they had had. The results are shown in Table. Does the students’ survey indicate that the standard deviation is greater than 0.75?

# of birthsFrequency0513021035

Short Answer

Expert verified

We do not reject the null hypothesis because the p-value is greater than the level of significance.

Step by step solution

01

Given Information

It is given that the number of births per woman in China is 1.6down from 5.91in 1966 and the data for the number of births by 50women is given.

Test whether the standard deviation of the number of births per woman in China is not greater than 0.75or not.

The null and alternative hypotheses are:

H0:σ=0.75

H1:σ>0.75

Therefore, the expected number of students to attend their graduation is 19.

02

Explanation

The calculation of mean and standard deviation is as shown below:

# of births(x)Frequency(f)x×fx2×f050013030302102040351545

Therefore, the mean and standard deviation will be calculated as:

x¯=fxn

=30+20+155+30+10+5

=1.3

s=x2fn-x¯2

=30+40+455+30+10+5-1.32

=0.61

The formula and calculation of the test statistic is:

χ2=(n-1)s2σ2

=(50-1)0.6120.752

=32.41

The degrees of freedom are 50-1=49. The formula and calculation of the p-value in Excel is:

Hence thep-value is0.9675

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