Question

The weight (in pounds) for a population of school-aged children is normally distributed with a mean equal to 133 ± 25 pounds (μ ± σ). Suppose we select a sample of 100 children (n = 100) to test whether children in this population are gaining weight at a 0.05 level of significance. Part (a) What are the null and alternative hypotheses? H0: μ ≤ 133 H1: μ > 133 H0: μ = 133 H1: μ < 133 H0: μ = 133 H1: μ ≠ 133 H0: μ ≤ 133 H1: μ = 133

Answer 1

Null hypothesis:
`\mu \leq 133`

Alternative hypothesis :
`\mu>133`

Explanation:

A hypothesis is defined as "a speculation or theory based on insufficient evidence that lends itself to further testing and experimentation. With further testing, a hypothesis can usually be proven true or false".

The null hypothesis is defined as "a hypothesis that says there is no statistical significance between the two variables in the hypothesis. It is the hypothesis that the researcher is trying to disprove".

The alternative hypothesis is "just the inverse, or opposite, of the null hypothesis. It is the hypothesis that researcher is trying to prove".

Data given and notation

`\bar X` represent the mean breaking strength value for the sample

`\sigma=25` represent the population standard deviation

`n=100` sample size

`\mu_o =133` represent the value that we want to test

`\alpha=0.01` represent the significance level for the hypothesis test.

z would represent the statistic (variable of interest)

`p_v` represent the p value for the test (variable of interest)

State the null and alternative hypotheses.

Is a one right tailed test.

What are H0 and Ha for this study?

We want to test if the children in this population are gaining weight, so we want to test if the mean increase from the reference value or no.

Null hypothesis:
`\mu \leq 133`

Alternative hypothesis :
`\mu>133`