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

Answer:

$\chi^2 =\frac{60-1}{64} 36 =33.19$

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.

Step-by-step 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: $\sigma^2 \neq 64$

The statistic is given by:

$\chi^2 =\frac{n-1}{\sigma^2_0} s^2$

Replacing we got:

$\chi^2 =\frac{60-1}{64} 36 =33.19$

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.