Question

Microplastics have been found in both tap water and bottled water.
Bottled water results A study analyzed 259 bottles and found an average of 320 plastic particles for every liter of water being sold. The associated standard deviation was 327. (Yes, the standard deviation is larger than the mean.)
Tap water results In a similar study, 30 tap water samples were analyzed. The average number of plastic particles found in each liter in the United States was 8.8 with a standard deviation of 2.3.
Conduct a hypothesis to evaluate if there is a difference between the average number of plastic particles in water bottles vs tap water.

What type of test should be run?

• Paired T-test
• 2 Sample T-test
• T-test
• 1 Proportion Z-test
• 2 Proportion Z-test

What are the hypotheses for this test?

• Ho: μ_bottled = μ_tap
  Ha: μ_bottled > μ_tap
• Ho: μ_bottled = μ_tap
  Ha: μ_bottled < μ_tap
• Ho: μ_bottled = μ_tap
  Ha: μ_bottled ≠ μ_tap

The test statistic for the hypothesis test is:  (please round to two decimal places)
The p-value for the hypothesis test is:  (please round to four decimal places)
Interpret the result of the hypothesis test in the context of the study:

• We reject the claim that the average number of plastic particles found in tap water and bottled water is the same.
• We fail to reject the claim that the average number of plastic particles found in tap water and bottled water is the same.

Answer 1

Here we want to run a two-sample t-test because both samples are independent.

Answer;-

• 2 Sample T-test

we want to conduct a hypothesis to evaluate if there is a difference between the average number of plastic particles in water bottles vs tap water.

μbottled: The average plastic particles for every liter of water being sold of bottles.

μtap: The average number of plastic particles found in each liter of tap water.

We want to test that there is a difference between the average number of plastic particles in water bottles vs tap water.

it is a non-directional test.

Ho: μbottled = μtap

vs
Ha: μbottled ≠ μtap

Interpret the result of the hypothesis test in the context of the study:

• We reject the claim that the average number of plastic particles found in tap water and bottled water is the same.