Question

A researcher tests the claim that the coronavirus can live on doorknobs for longer than on stainless steel water bottles, on average.

1. Write the null and alternative hypotheses.

2. If the researcher commits a Type I error, that means the researcher rejects the null hypothesis when the null hypothesis is true (i.e. the alternative hypothesis is false). Write the Type I error in context.

3. If the researcher commits a Type II error, that means the researcher fails to reject the null hypothesis when the null hypothesis is false (i.e. the alternative hypothesis is true). Write the Type II error in context.

4. If α=0.05 and p-value = 0.017, write the conclusion in context.

Answer 1

1.). Let X = Researcher's claim time for which coronavirus live on doorknobs.

U = Average time for which coronavirus should live on stainless steel water bottles.

Null hypothesis( Ho) : X = U

Alternative hypothesis ( Ha) : X > U

2.). Yes , it is true that type 1 error occurs when we reject the null hypothesis even though it is true ie alternative hypothesis is false. It is equal to the significance level given in question . We have two types of region in hypothesis curve . Type 1 error occurs when we reject the null hypothesis even though it is lying in confidence interval.

In the above context we have found that average time for which coronavirus live on doorknobs is same as the time for which it lives on water bottles. But due to type 1 error we have rejected this claim and falsly accepted that there is difference in both the claims.

3. Type 2 error occurs when we fail to reject the null hypothesis even though it is false and it should have been rejected. So this is correct statement. It occurs when our p value lies in the rejection region , it should have rejected the null hypothesis and accepted the alternative hypothesis. But we fail to reject the null hypothesis . So here we are making type 2 error.

As per researcher' s context they have found that average time for coronavirus living on doorknobs is greater than that of water bottles ,we should have accepted the alternate hypothesis rejecting the null hypothesis. But due to type 2 error we do not reject null hypothesis and we accept falsly that these both times are same.

4.). Here alpha value is 0.05 , p value is 0.017

As per the law of hypothesis testing , we reject the null hypithesis if our p value is less than the significance level and vice versa.

Here p value is less than significance level , so we need to reject the null hypothesis.

As per above context , we reject the null hypothesis. It means the researchers have found that time for coronavirus living on doorknobs is greater than that of stainless steel waterbottles.