Question

7. For any hypothesis test: b) Write down the appropriate alternative hypotheses and give the formula for the each test statistic, if any, for the following null hypothesis testing population normally distributed population not normal population not normal population not normal population normal population normal population not normal () Ho: So n 80, s 29 (iii) Ho: μ-Ha n-15, σ-25 (iv) Ho: μ=Ha n= 15, s = 36 (v) Ho: μ>Ha n= 10, σ = 16 (vi) H0'μ Han-60, σ-81 (vii) H0' μ-Hon 200, s-25

Answer 1

(a)

When in statistics hypothesis test is conducted and researcher has small doubt the results, the null hypothesis get the benefit of doubt. The first step in the hypothesis testing is to decide the research question.

According to research question person needs to define the hypotheses. After that he needs to collect data. On the basis of data we need to find which hypothesis is statistically significant. The test is started by making assumption that null hypothesis is true. Equal to sign always goes into null hypothesis.

The null hypothesis assumes that there is no difference between the two groups being compared or parameter is equal to specified value.

The alternative hypothesis assumes that there is a difference between the two groups being compared or parameter is not equal to specified value.

(b)(i)

$H_{a}:\mu\neq \mu_{0}$

Since population is normally distributed so t test can be used. The test statistics is

$t=\frac{\bar{x}-\mu_{0}}{s/\sqrt{n}}$

(ii)

$H_{a}:\mu> \mu_{0}$

Since population is not normally distributed but sample size is greater than 30 so t test can be used. The test statistics is

$t=\frac{\bar{x}-\mu_{0}}{s/\sqrt{n}}$

(iii)

$H_{a}:\mu\neq \mu_{0}$

Since population is not normally distributed and sample size is less than 30 so no test statistics can be applied.

(iv)

$H_{a}:\mu\neq \mu_{0}$

Since population is not normally distributed but sample size is greater than 30 so t test can be used. The test statistics is

$t=\frac{\bar{x}-\mu_{0}}{s/\sqrt{n}}$

(v)

$H_{a}:\mu< \mu_{0}$

Since population is normally distributed so z test can be used. The test statistics is

$z=\frac{\bar{x}-\mu_{0}}{\sigma/\sqrt{n}}$

(vi)

$H_{a}:\mu> \mu_{0}$

Since population is normally distributed so z test can be used. The test statistics is

$z=\frac{\bar{x}-\mu_{0}}{\sigma/\sqrt{n}}$

(vii)

$H_{a}:\mu\neq \mu_{0}$

Since population is not normally distributed but sample size is greater than 30 so t test can be used. The test statistics is

$t=\frac{\bar{x}-\mu_{0}}{s/\sqrt{n}}$