Question

1. Hypothesis Testing - Setup: Suppose you want to test the claim that the mean volume in all 12-ounce cans of Fizzy Pop soda is equal to 12 ounces. In a sample of 120 cans, you find the sample mean is 12.2 ounces.

(a) What is the claim?

μ < 12

μ > 12    

μ = 12

μ = 12.2
(b) What does μ represent?

the proportion of all cans with a volume = 12 ounces

the mean volume of all 12-ounce cans of Fizzy Pop   

the mean volume of all 120 cans from the sample
(c) What is the null hypothesis?

μ < 12

μ > 12  

μ = 12

μ = 12.2
(d) What is the alternate hypothesis?

μ < 12

μ > 12   

μ ≠ 12

μ = 12.2
(d) What type of test is this?

left-tailed

right-tailed   

two-tailed

2.

Similar Tests - Assembly Time: You manufacture boxed swing sets and want to convince customers that it takes less than 2 hours to assemble one. You take a sample of adults, have them assemble the swing sets, and time them. About 78% of the adults get done in just under 2 hours but the other 22% take much more than 2 hours. You are considering the two claims given below. For each claim, choose the appropriate alternate hypothesis for the test.

(a) You claim that most adults take less than 2 hours to assemble the swing set.

H₁: μ < 2

H₁: p > 0.5    

H₁: x < 2

H₁: p < 2
(b) You claim that the average assembly time is less than 2 hours.

H₁: p < 2

H₁: x < 2    

H₁: p > 0.5

H₁: μ < 2

3. Similar Tests - Facebook Friends: You want to test the following similar claims about the number of Facebook friends that college students have.
For each test, choose the appropriate null hypothesis.

(a) Claim: The average number of Facebook friends for college student users is greater than 254.
Choose the appropriate null hypothesis.

H₀: x = 254

H₀: p = 254   

H₀: p = 0.5

H₀: μ = 254
(b) Claim: Most college student Facebook users have more than 254 Facebook friends.
Choose the appropriate null hypothesis.

H₀: μ = 254

H₀: p = 254  

H₀: x = 254

H₀: p = 0.5

Answer 1

Solution :

1)

(a)

Claim :

= 12

(b)

the mean volume of all 12-ounce cans of Fizzy Pop  

(c)

The null hypothesis is ,

H₀ :   = 12

(d)

The alternative hypothesis is,

H_a :    12

(e)

This is the two tailed test .