Question

1.A fast-food chain claims that the fat content of one of its cheeseburgers is 22 grams. A consumer health group wanted to check this claim, so it obtained a random sample of 20 cheeseburgers from the chain and measured the fat content. The fat contents (in grams) are shown below, rounded to the nearest gram.

Use Excel to test whether the mean fat content is different from 22 grams. Identify the p-value from the output, rounding to three decimal places.

23
21
21
21
21
23
24
23
22
22
22
22
25
22
24
23
24
24
23
23

2.

Which of the following answers give valid null and alternative hypotheses for a hypothesis test?

Select all correct answers.

Select all that apply:

• H0:μ=15; Ha:μ≤15

• H0:μ=15; Ha:μ<15

• H0:μ=15; Ha:μ≠15

• H0:μ≠15; Ha:μ=15

• 3. A researcher claims that the incidence of a certain type of cancer is less than 5%. To test this claim, the a random sample of 4000 people are checked and 170 are determined to have the cancer.

  The following is the setup for this hypothesis test:

  {H0:p=0.05 Ha:p<0.05

• Find the test statistic for this hypothesis test for a proportion. Round your answer to 2 decimal places.

Answer 1

1 ) let us consider H0 :

H1 :

since the sample size is less than 30 so we will use t test in minitab for one samle

we have the following output

One-Sample T: cheesburgers

Test of μ = 22 vs ≠ 22

Variable N Mean StDev SE Mean T P
cheesburgers 20 22.650 1.182 0.264 2.46 0.024

the p value is 0.024

2 ) the correct hypothesis setups are

• H0:μ=15; Ha:μ<15

• H0:μ=15; Ha:μ≠15

3 )H0:p=0.05

Ha:p<0.05 ( left tailed )

using the minitab for 1 sample proportion we have the output

Test of p = 0.05 vs p < 0.05

Sample X N Sample p 95% Upper Bound Z-Value P-Value
1 170 4000 0.042500 0.047746 -2.18 0.015

test statistic is -2.18