Question

It has been hypothesized that the standard deviation of the germination time of radish seeds is 8 days. The standard deviation of a ran- dom sample of 60 radish plants’ germination times was 6 days. At α = 0.01, test the claim.

Answer 1

`\chi^2 =(60-1)/(64) 36 =33.19`

The degrees of freedom are:

`df= n-1= 60-1= 59`

And the p value would be given by:

`p_v =2*P(\chi^2 >33.19)=0.0053`

Since the p value is lower than the significance level we have enough evidence to reject the null hypothesis and we can conclude that the true deviation is different from 8 days.

Explanation:

Data given

`n=60` represent the sample size

`\alpha=0.01` represent the confidence level

`s^2 =6^2 =36` represent the sample variance obtained

`\sigma^2_0 =8^=64` represent the value that we want to test

Hypothesis to test

We want to verify if the true deviation is equal to 8 days o not, so the system of hypothesis would be:

Null Hypothesis:
`\sigma^2 = 64`

Alternative hypothesis:
`\sigma^2 \\eq 64`

The statistic is given by:

`\chi^2 =(n-1)/(\sigma^2_0) s^2`

Replacing we got:

`\chi^2 =(60-1)/(64) 36 =33.19`

The degrees of freedom are:

`df= n-1= 60-1= 59`

And the p value would be given by:

`p_v =2*P(\chi^2 >33.19)=0.0053`

Since the p value is lower than the significance level we have enough evidence to reject the null hypothesis and we can conclude that the true deviation is different from 8 days.