The process that produces sonora bars (a type of candy) is intended to produce bars with a mean weight of 56 gm. the process standard deviation is known to be 0.77 gm. a random sample of 49 candy bars yields a mean weight of 55.82 gm. which are the hypotheses to test whether the mean is different than it is supposed to be? assume that candy bar weights are normally distributed.
select one:
a. h0: μ ≤ 56, ha: μ > 56
b. h0: μ ≥ 56, ha: μ < 56
c. h0: μ = 56, ha: μ ≠ 56
d. h0: μ < 56, ha: μ ≥ 56

c. H0: μ = 56, HA: μ ≠ 56

Step-by-step explanation:

A hypothesis is defined as "a speculation or theory based on insufficient evidence that lends itself to further testing and experimentation. With further testing, a hypothesis can usually be proven true or false".  

The null hypothesis is defined as "a hypothesis that says there is no statistical significance between the two variables in the hypothesis. It is the hypothesis that the researcher is trying to disprove".

The alternative hypothesis is "just the inverse, or opposite, of the null hypothesis. It is the hypothesis that researcher is trying to prove".

1) Data given and notation      

represent the mean weight for the Canby Bars

represent the standard deviation for the population    

sample size      

represent the value that we want to test    

represent the significance level for the hypothesis test.    

z 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 determine if the mean is different than it is supposed to be (56), the system of hypothesis would be:    

Null hypothesis:      

Alternative hypothesis:      

We know the population deviation, so for this case is better apply a z test to compare the actual mean to the reference value, and the statistic is given by:      

(1)      

z-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:      

Calculate the P-value      

Since is a one-side lower test the p value would be:      

Conclusion      

If we compare the p value and the significance level given for example we see that so we can conclude that we FAIL to reject the null hypothesis, and the the actual mean weight not differs significantly from the standard 56.      

infinitely many solutions

step-by-step explanation:

we have been given the equation;

2(2x + 3) = -4 + 2(2x + 5)

we need to determine the value of x.

2(2x + 3), we expand this expression to obtain 4x + 6

similarly 2(2x + 5) will become 4x + 10

now we have;

4x + 6 = -4 + 4x + 10

4x + 6 = 4x + 10 - 4

4x + 6 = 4x + 6

the expression on the left hand side is identical to the one on the right hand side. therefore, we are looking at just a single straight line whose equation is;

y = 4x + 6

consequently, we shall have infinitely many solutions

the answer is two. hope this !