Determine the decision criterion for rejecting the null hypothesis in the given hypothesis test. describe the values of the test statistic that would result in rejection of the null hypothesis. a cereal company claims that the mean weight of the cereal in its packets is at least 14 oz. you wish to test this claim at the 0.02 level of significance. the mean weight for the random sample of 45 cerial packets is 13.8 oz with a standard deviation of 0.3 oz. what criterion would be used for rejecting the null hypothesis, that oz ? reject h0 if test statistic < 2.05. reject h0 if test statistic > -2.05. reject h0 if test statistic < -2.05. reject h0 if test statistic < -2.33.

We can assume that the sample size is large enough to use the z distribution as an approximation of the t distribution

Now we need to find on the z distribution a value that accumulates 0.02 of the area on the left and this value is

We can use the following excel code to verify it: "=NORM.INV(0.02,0,1)"Reject H0 if test statistic < -2.05

And for our case our calculated value <-2.05 so we have enough evidence to reject the null hypothesis at 2% of significance.

Step-by-step explanation:

Data given and notation  

represent the sample mea   n

represent the sample standard deviation

sample size  

represent the value that we want to test

represent the significance level for the hypothesis test.  

t would represent the statistic (variable of interest)  

represent the p value for the test (variable of interest)  

State the null and alternative hypotheses.  

We need to conduct a hypothesis in order to check if the mean is at least 14 oz, the system of hypothesis would be:  

Null hypothesis:  

Alternative hypothesis:  

If we analyze the size for the sample is > 30 but we don't know the population deviation so is better apply a t test to compare the actual mean to the reference value, and the statistic is given by:  

 (1)  

t-test: "Is used to compare group means. Is one of the most common tests and is used to determine if the mean is (higher, less or not equal) to an specified value".  

Calculate the statistic

We can replace in formula (1) the info given like this:  

Critical region

We can assume that the sample size is large enough to use the z distribution as an approximation of the t distribution

Now we need to find on the z distribution a value that accumulates 0.02 of the area on the left and this value is

We can use the following excel code to verify it: "=NORM.INV(0.02,0,1)"

So then the correct answer for this case would be:

Reject H0 if test statistic < -2.05

And for our case our calculated value <-2.05 so we have enough evidence to reject the null hypothesis at 2% of significance.

something that characterises a right triangle is the fact that we may use pythagoras' theorem to find any one of its sides given that we have the length of the other two sides. here, we have the length of the hypotenuse, √(87) yd, and one other side, √(23) yd, thus we can easily find the length of the remaining side using pythagoras' theorem as defined below:

c^2 = a^2 + b^2, where c is the length of the hypotenuse, and a and b are the lengths of the other two sides.

thus, given that c = √(87) and a = √(23), we may substitute these into the formula we defined above to get:

c^2 = a^2 + b^2

(√87)^2 = (√23)^2 + b^2 (substitute c = √87 and a = √23 into the equation)

87 = 23 + b^2 (evaluate (√87)^2 = 87 and (√23)^2 = 23 - remember that the square root of a number, squared will equal that very same number)

64 = b^2 (subtract 23 from both sides)

√64 = b (take the square root of both sides)

8 = b (evaluate √64 = 8)

therefor, the length of the unknown leg in the right triangle is 8 yd (first answer).

that is the sum

step-by-step explanation:

there are no other answers without knowing the variables values