I need some help on a stat assignment from SNHU MAT-243. Hypothesis Testing for the Difference Between Two Population Parameters. The prompt says:

Suppose that the factory claims that the proportion of ball bearings with diameter values less than 2.20 cm in the existing manufacturing process is the same as the proportion in the new process. At alpha=0.05, is there enough evidence that the two proportions are the same? Perform a hypothesis test for the difference between two population proportions to test this claim.

1. Define the null and alternative hypotheses in mathematical terms as well as in words.
2. Identify the level of significance.
3. Include the test statistic and the P-value. See Step 2 in the Python script. (Note that Python methods return two tailed P-values. You must report the correct P-value based on the alternative hypothesis.)
4. Provide a conclusion and interpretation of the test: Should the null hypothesis be rejected? Why or why not?

The only data given is this:

test-statistic = 1.1881 two tailed p-value = 0.23479

I have, I think, done the work properly but the double negative nature of failing to reject the hypothesis has me going bonkers. Here is what I have:

Hi Everyone,

This week's prompt is about a factory producing ball bearings. They have a new process for manufacture and have stated the the new process produces the same proportion of ball bearings where the diameter of the ball is less than 2.20 cm. This week's Python created some data for this experiment, in two data samples of 50 observations each representing the old and new manufacturing processes. The second part of the Python script ran the z_test and output the z_test test statistic value, in my case 1.1881, and the two tailed p-value which, in my case, was 0.23479.

The discussion prompt has asked for some analysis using this information in four steps:

Define the null and alternative hypotheses in mathematical terms as well as in words.

The null hypothesis is that the proportion of bearings less than 2.20 cm to those greater than or equal to that diameter is the same in both the old and new processes. Mathematically this can be expressed as P₁=P_2. If this were true then the factory's assertion is correct.

The alternative hypothesis is that the two proportions are not equal and that one process is producing more bearings less than 2.20 cm than the other process. Mathematically this can be expressed as P₁ P₂.

Identify the level of significance.

The level of significance is 0.05 (alpha=0.05 is stated in the prompt.)

Include the test statistic and the P-value. See Step 2 in the Python script.

test_statistic, p_value = proportions_ztest(counts, n)

print("test-statistic =", round(test_statistic,4)) print("two tailed p-value =", round(p_value,5))

test-statistic = 1.1881 two tailed p-value = 0.23479

The test statistic z value from my Python run was 1.1881. The two tailed p-value provided by the Python script was 0.23479. That seems correct to use the two tail p-value since the alternative hypothesis is that the P₁ P_2, or in other words that means the true value could be more or less. More + Less = Two Tailed. The 0.05 significance means we are working with a 95% confidence, so that leaves us with a rejection range of 0.025 on either side of the distribution, which is the 5% or 0.05 divided by two so we have a value for each side's rejection limit. Our two tailed p-value was 0.23479, so we divide that by 2 for a one tailed p-value of 0.117395. 0.117395 is greater than 0.05 which means we are outside the 95% confidence zone and are unable to reject the null hypothesis.

Provide a conclusion and interpretation of the test: Should the null hypothesis be rejected? Why or why not?

Our P-Value is greater than 0.05 so we are unable to reject the NULL hypothesis. If you find this double negative wording annoying you could phrase is as "the proportion of balls that are less than 2.20 cm with the new process is not the same as it was in the old process."

Cheers,

Matt