On a can of sardines it is written that the can contains 10 sardines. You open up 100 cans and find the average is 9.75 sardines with a standard deviation of 1.
What is the test statistic in a test of the null hypothesis that the population average is 10?

Step-by-step explanation:

By considering the given statements :

Null hypothesis :

Alternative hypothesis :           ( opposite of null hypothesis.)

As per given , we have

Sample size : n= 100

Sample mean :

Sample standard deviations :

Since population standard deviation is unknown , so we will perform t-test.

Formula for test statistic ( for population mean):

Hence, the required test statistic :

x = ±sqrt(10)

step-by-step explanation:

5 - 2x² = -15

subtract 5 from each side

5-5 - 2x² = -15-5

-2x^2   = -20

divide by -2 on each side

-2x^2   /-2= -20/-2

x^2 =10

take the square root on each side

sqrt(x^2 )=±sqrt(10)

x = ±sqrt(10)

check:

5 - 2x² = -15

+sqrt(10)

5 - 2(sqrt(10))² = -15

5 -2(10) = -15

5 -20 = -15

-15 = -15

-sqrt(10)

5 - 2(-sqrt(10))² = -15

5 -2(10) = -15

5 -20 = -15

-15 = -15

the first option is the answer.