Question

3. Heights of 1-year-old girls are Normally distributed, with mean 30 inches and standard deviation of 1.2 inches. A company claims that taking 500 mg of vitamin C makes girls taller. In a random sample of 100 baby girls who were given 500 mg vitamin C daily from birth to 1 year, the mean height was 30.1 inches. Is this evidence for the company’s claim? Assume the standard deviation remains the same. To make this determination, calculate and interpret the p-value for the appropriate test.

Answer 1

The p- value is
`p-value  =  0.2033`

Its interpretation is

As
`p-value > \alpha`

The decision rule is

Fail to reject the null hypothesis

The conclusion is

There is no sufficient evidence to support the company claims at a level of sign9ificance of 0.05

Explanation:

From the question we are told that

The mean is
`\mu =  30 \  inches`

The standard deviation is
`\sigma  =  1.2 \  inches`

The sample size is n = 100

The sample mean is
`\= x  =  30.1`

Let assume the level of significance is
`\alpha = 0.05`

The null hypothesis is
`H_o  :  \mu \le 30`

The alternative is
`H_a : \mu > 30`

Generally the test test is mathematically represented as

`z =  (\= x- \mu )/((\sigma)/(√(n) ) )`

=>
`z =  (30.1- 30 )/((1.2)/(√(100) ) )`

=>
`z =  0.83`

Generally from the z-table the probability of (Z > 0.83 ) is

`p-value  =  0.2033`

From the value obtained we see that
`p-value > \alpha` hence

The decision rule is

Fail to reject the null hypothesis

The conclusion is

There is no sufficient evidence to support the company claims at a level of sign9ificance of 0.05