Question

For Hypothesis testing and Decision making problems, please do the following:

1. State the null and alternate hypothesis.

2. Write down the proper test statistic.

3. Show all calculations.

4. Show the critical value.

(5. State your conclusions.

1a. In a study of children with congenital heart disease, researchers gathered data on age (in months) of ‘first’ walking from 16 children with acyanotic heart disease. From larger studies on normal children, the researchers know that mean age of walking for normal children is 12.0 months (µ) and that the standard deviation is 1.75 months ( σ). The researchers wish to decide whether or not acyanotic children learn to walk at the same age on the average as normal children. The 16 children had an average age of walking of 13.0 .

Test by hypothesis at the 5% level of significance. Assume data is continuous and normally distributed.

1b. Write down the appropriate formula for a (1- α) % confidence interval, but you do not need to calculate.

Answer 1

Let denotes the mean age of walking for acyanotic children.

The null and alternate hypothesis are :

against

Here

sample mean

population standard deviation

and sample size

The test statistic can be written as

which under H₀ follows a standard normal distribution.

We reject H₀ at 5% level of significance if

Now,

The value of the test statistic

and critical value

Since so we reject H₀ at 5% level of significance and we can conclude that acyanotic children learn to walk at significantly different age on the average as normal children

The (1- α) % confidence interval of mean age of walking for acyanotic children