Question

A sociologist studying the difference in ages between husbands and wives obtained a random sample of 55 married couples. The mean of the husbands’ ages was 38.5 years with standard deviation 12.6 years. The mean of the wives’ ages was 36.9 years with standard deviation 12.4 years. The sociologist calculated the difference between the ages for each couple. The mean difference was 1.6 years with standard deviation 2.1 years. A matched-pairs hypothesis test will be performed to investigate whether the difference is significant.

Answer 1

Answer:

2.1/√55

Step-by-step explanation:

simga divided by sample size

Answer 2

You can use the definition of standard error to calculate the standard error in this case.

The standard error of the sampling distribution is $\dfrac{2.1}{\sqrt{55}}$

How to calculate the standard error of the sampling distribution if matched pair t test is performed?

Standard error shows the variability of the test statistic. Here it is the difference in the mean.

The standard error for this large sample(n=55) can be calculated by $\dfrac{s_d}{\sqrt{n}}$ where the value n is the sample size and $s_d$ is the standard deviation of the test statistic.

Thus, by using above formula, we have:

SE = $\dfrac{s_d}{\sqrt{n}} = \dfrac{2.1}{\sqrt{55}}$

Thus,

The standard error of the sampling distribution is $\dfrac{2.1}{\sqrt{55}}$

Learn more about standard error here:

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