Question

One of your friends is testing the effect of drinking coffee on the duration of cold symptoms. The common cold lasts, on average, 6 days. Your friend starts with no expectations as to whether drinking coffee will have any effect on cold duration. After seeing the results of the experiment, in which the average cold duration was less than 6 days, your friend tests a one-sided alternative about the population mean cold duration when drinking coffee,H0: μcoffee = 6Ha: μcoffee < 6She finds z = â1.68 with one-sided P-value P = 0.0465.What is the correct two-sided P-value for z = â1.68? Round your answer to 4 decimal places.

Answer 1

Null hypothesis:
`\mu \geq 6`

Alternative hypothesis:
`\mu <6`

For this case after conduct the one lower tail test we got the following p value:

`p_v = P(t <-1.68) = 0.0465`

And for this case if we want to conduct a bilateral test or two sided the sytem of hypothesis are:

Null hypothesis:
`\mu = 6`

Alternative hypothesis:
`\mu \\eq 6`

And for this case the p value can be calculated like this:

`p_v = 2* P(t <-1.68) =2* 0.0465= 0.0930`

Explanation:

For this case we are trying to proof the following system of hypothesis:

Null hypothesis:
`\mu \geq 6`

Alternative hypothesis:
`\mu <6`

For this case after conduct the one lower tail test we got the following p value:

`p_v = P(t <-1.68) = 0.0465`

And for this case if we want to conduct a bilateral test or two sided the sytem of hypothesis are:

Null hypothesis:
`\mu = 6`

Alternative hypothesis:
`\mu \\eq 6`

And for this case the p value can be calculated like this:

`p_v = 2* P(t <-1.68) =2* 0.0465= 0.0930`