Respuesta :
Answer:
Yes, there is evidence to support the belief that the mean is less than 15.25 ounces.
Step-by-step explanation:
We are given that for a certain brand of canned corn, the company claims that the mean weight of the contents of the cans is 15.25 ounces. A random sample of 36 cans were selected. The sample was found to have mean 15.18 ounces and standard deviation 0.12 ounce.
We have to test the hypothesis that the mean is less than 15.25 ounces or not.
Let [tex]\mu[/tex] = mean weight of the contents of the cans
So, Null Hypothesis, [tex]H_0[/tex] : [tex]\mu \geq[/tex] 15.25 ounces {means that the mean is more than or equal to 15.25 ounces}
Alternate Hypothesis, [tex]H_a[/tex] : [tex]\mu[/tex] < 15.25 ounces {means that the mean is less than 15.25 ounces}
The test statistics that will be used here is One-sample t-test statistics;
T.S. = [tex]\frac{\bar X -\mu}{\frac{s}{\sqrt{n} } }[/tex] ~ [tex]t_n_-_1[/tex]
where, [tex]\bar X[/tex] = sample mean weight = 15.18 ounces
s = sample standard deviation = 0.12 ounces
n = sample of cans = 36
So, test statistics = [tex]\frac{15.18-15.25}{\frac{0.12}{\sqrt{36} } }[/tex] ~ [tex]t_3_5[/tex]
= -3.5
Now, since we are not given with the level of significance in the question so we assume it to be 5%. At 5% significance level, the t table gives critical value of -1.6895 at 35 degree of freedom. Since our test statistics is way less than the critical value of t so we have sufficient evidence to reject our null hypothesis as it will fall in the rejection region.
Therefore, we conclude that the mean is less than 15.25 ounces and which means there is evidence to support the company belief that the mean is less than 15.25 ounces.
Hypothesis test-an idea that is suggested as the possible explanation for something but has not yet been found to be true or correct. Thus, the alternate hypothesis test is correct answer to these question.
Types
- Null hypothesis
- Alternate Hypothesis
The test can be conducted on two basis that are mentioned below.
- Null hypothesis it should be greater than the weight of net 15.25 ounces.
- After investigating the random sample of 36 cans mean weight is coming 15.18 ounces that is alternate hypothesis test is correct which is less than the 15.25 and the significance level is coming in the negative side and its not mention in the Question.
- 15.18-15.25= -0.07*0.2= -.014.
- Therefore, we conclude that the mean is less than 15.25 ounces and which means there is evidence to support the company belief that the mean is less than 15.25 ounces.
Therefore, the alternate hypothesis test is correct answer to these question.
To know more about these above mentioned:
https://brainly.com/question/1762050
