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. she starts with no expectations as to whether drinking coffee will have any effect at all on cold duration. after seeing the results of her experiment, in which the average cold duration was less than 6 days, she tests a one-sided alternative about the population mean cold duration when drinking coffee,

h0: μcoffee = 6

ha: μcoffee < 6

she finds z = −1.68 with one-sided p-value p = 0.0465.

what is the correct two-sided p-value for z = −1.68? round your answer to 4 decimal places.

0.0930

Step-by-step explanation:

As per given , we have

H0: μcoffee = 6

Ha: μcoffee < 6

She finds z = −1.68 with one-sided P-value P = 0.0465.

The P-value for two-tailed test is calculated by :

For z= -1.68 , we have

Hence, the correct two-sided P-value for z = −1.68 is 0.0930 .

let's cover over the formula of the vertex:

y = a(x – h)^2 + k

in this formula, (h,k) are the vertex, always remember that the positive or negative value of the vertex is based on the sign it has.

for example, if the vertex is -3,-6 then both the x and y value would have the positive sign attached to it and if it were a positive x and y value, then a negative sign would be attached to it.

with that being said, for our problem the x value is a positive one so we are looking for a number with a negative sign next to it, in this case the first and second choice.

however, for the first answer choice it isn't quite part of the formula so we know that the answer choice correctly displays the x value.

to confirm, we can see if the -1 fits correctly with the second answer choice, and as mentioned above a negative number will have a positive sign attached to it. so, for our problem we can see that -1 has been changed to +1, so we can confirm that the second answer choice is correct.

hence, our final answer is y=(x - 1)^2 + 1