STA 210-7521 Spring 17 Homework: Section 7.2 Lecture Video & Homework Score: 2 o
ID: 3180741 • Letter: S
Question
Explanation / Answer
a) Identify the null hypothesis and alternative hypothesis.
To find the null and alternative hypothesis, start by writing the claim mathematically. The claim, “the mean tuna consumption by a person is 3.1 pounds per year.” Expressed mathematically is µ = 3.1
The order hypothesis is the complement of the claim. The complement of µ = 3.1 is µ 3.1.
The null hypothesis H0 is a statement that contain a statement of equality, such as , =, or .
The alternative hypothesis Ha is the complement of the null hypothesis. It is a statement that must be true if is false, and it contain a statement of inequality, such as < , , or >. Thus, H0 and Hacan be stated as follows.
H0: µ = 3.1
Ha : µ 3.1
b)z-statistic=(x bar-mu)/(sigma/sqrt(n))
so (2.9-3.1)/(1.19/sqrt(50))=-1.19.
c)P-value:
In order to find the P-value, first determine if the hypothesis test is left-tailed, right-tailed, or two-tailed. The test is two-tailed.
You can either use a standard normal distribution table or technology to find the p-value. For this explanation, a standard normal distribution table is used.
Since the test is two-tailed, the P-value is equal to twice the are in the tail of the standardized test statistic z = -1.19. Because z is negative, the tail is on the left. Use a standard normal distribution table to find the area to the left of z = -1.19.
The area to the left of z = -1.19 is 0.117
Now double the area in the left tail to find the P-value, rounding to three decimal places.
P-value = 0.2340
Since P-value>significance value so we fail to reject the null hypothesis.
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