Question

Is the mean age at which American children learn to walk less than 15 months? A study of 40 American children found a mean walking age of = 13.2 months. If the population of all American children has mean age μ until they begin to walk and standard deviation σ, which of the following null and alternative hypotheses should we test to answer this question? H 0 : μ ≥ 13.2 vs. Ha : μ < 13.2 H 0 : μ = 13.2 vs. H a : μ ≠ 13.2 H 0 : μ = 15 vs. H a : μ ≠ 15 H 0 : μ ≥ 15 vs. Ha : μ < 15

Answer 1

We define the random variable X as the walking age and we are interested if American children learn to walk less than 15 months so then that would be the alternative hypothesis and the complement would be the null hypothesis.

Null hypothesis:
`\mu \geq 15`

Alternative hypothesis:
`\mu <15`

And for this case the best answer would be:

H 0 : μ ≥ 15 vs. Ha : μ < 15

Explanation:

We define the random variable X as the walking age and we are interested if American children learn to walk less than 15 months so then that would be the alternative hypothesis and the complement would be the null hypothesis.

Null hypothesis:
`\mu \geq 15`

Alternative hypothesis:
`\mu <15`

And for this case the best answer would be:

H 0 : μ ≥ 15 vs. Ha : μ < 15

And the data given from the sample is:

`\bar X = 13.2` represent the sample mean

`\sigma` represent the population deviation

`n = 40` represent the sample size

And the statistic would be given by:

`z = (\bar X -\mu)/((\sigma)/(√(n)))`