I want response for these two posts

How do their confidence intervals compare with yours?

f the population standard deviation is unknown and the sample size is not sufficiently large, would you still use the Normal distribution to calculate these confidence intervals, or would you choose another distribution? If the latter, which distribution would you choose?

1==

1. The confidence levels are:
   1. 90% - 2.26, 2.50
   2. 99% - 2.20, 2.56
2. The 90% confidence interval is telling us that there is an estimation that the average diameter of the ball bearing is between 2.26cm and 2.50cm. Where in the 99% confidence interval is saying that there is an estimation that the average diameter of the ball bearing is between 2.20cm and 2.56cm.
3. The null hypothesis for this test is that the average diameter of the ball bearing is 2.30cm while the alternative hypothesis is that the average diameter of the ball bearing is greater than 2.30cm. In mathematical terms, the null hypothesis is that the average diameter = 2.30cm or H0=2.30 cm. For the alternative hypothesis, the mathematical term for it would be average diameter 2.30cm or Ha 2.30cm.
4. z-test hypothesis test for population mean test-statistic = 1.04 two tailed p-value = 0.3006
5. The level of significance is not statistically significant because if you look at the p-value you can notice that it is greater than 0.01. This means that the null hypothesis shouldn't be rejected because the p-value is not less than or equal to the significance level meaning the sample data is in favor of the alternative hypothesis.

2----

The first step of constructing the confidence intervals was generating the sample data. The 50 samples that were generated ranged between 1 and 4. The confidence intervals that were generated from these are:

90% confidence interval (rounded) = ( 2.37, 2.61 )

99% confidence interval (rounded) = ( 2.31, 2.67 )

A confidence interval is a range of values likely to contain the parameter being estimated along with a probability statement. It is another way to describe probability. In this case, it means that we can be 90% confident that the parameter is within the values 2.37-2.61. And we can be almost certain that the parameter lies within the values 2.31-2.67. The 90% confidence interval is closer together because it becomes more difficult to mathematically estimate the data as a more precise value.

It has been claimed from previous studies that the average diameter of the ball bearings from this manufacturing process is 2.30 centimeters. Based on this sample of 50 that I collected, there is evidence to suggest that the average diameter is greater than 2.30 centimeters. I gathered this from the confidence intervals. Both of the lower values are greater than 2.30.

The null hypothesis for the test here would be that the average diameter of the ball bearings is 2.30 centimeters.

null hypothesis: =2.30

The alternative hypothesis would be that the diameter of the ball bearings is greater than or less than 2.30 centimeters.

alt hypothesis: 2.30

The level of significance: A = 0.01

The test statistic is calculated to be:

test-statistic = 2.7

Since the alternative hypothesis is either greater than or less than the null hypothesis, it will be a two-tailed hypothesis. This is calculated to be:

two-tailed p-value = 0.0069

Since the p-value is less than the level of significance, the resulting value is statistically significant. This means that the null hypothesis should be rejected, and the alternative hypothesis should be accepted.