Question

The null and alternative hypotheses are given. Determine whether the hypothesis test is​ left-tailed, right-tailed, or​ two-tailed. What parameter is being​ tested?

Upper H0​: sigmaσ equals= 99
Upper H1​: sigmaσ not equals≠ 99
What type of test is being conducted in this​ problem?

Answer 1

Two tailed test

Parameter tested= population standard deviation

Explanation:

1) Important concepts

The chi-square test if the standard deviation of a population is equal to a given value. We can conduct the test two-side or a one-side.

For the case of two-side we want to check if the population deviation is equal to some value or no. And for the case of one-side we want to check if the population devition is higher or lower than a given value.

The system of hypothesis are:

`\sigma=\sigma_o` Null hypothesis

`\sigma \\eq \sigma_o` Alternative hypothesis

That's when we use the two sided version but we can have other's alternative hypothesis if we use one-side test:

`\sigma < \sigma_o` Alternative hypothesis

`\sigma > \sigma_o` Alternative hypothesis

The test statistic to check the hypothesis is:

`t=(N-1)((s)/(\sigma_o))^2`

For this special case the value of
`\sigma_o =99`

Where N represent the sample size and s is the sample standard deviation. The ratio
`(s)/(\sigma_o)` is important since allows to compare the ratio of the sample standard deviation to the specified value. If this ratio is different from 1, we will have evidence that we can reject the null hypothesis.

Using a significance level
`\alpha` we can find the critical region for the possible alternative hypothesis:

`t>\chi_(\alpha,N-1)^2` for the upper one tailed option

`t<\chi_(1-\alpha,N-1)^2` for the lower one tailed option

`t<\chi_{1-(\alpha)/(2),N-1}^2` for the two tailed option

The N-1 represent the degrees of freedom for the chi square distribution.

2) Solving the question

Based on all the info from above we can conclude that:

Type of test= Two tailed test

Parameter tested=population Standard deviation

And they want to check if the population deviation differs from 99