It looks like you've uploaded a file with some data related to a statistical hypothesis test. Let me first extract the necessary information and then proceed with solving the problems you mentioned.

I'll begin by analyzing the data provided in the image, and then answer each part of the question.

I'll start with part (a) and check if the data follows a normal distribution. Then I'll move on to other parts after that.

Let me process the data first.The data provided in the image consists of the nicotine content in milligrams for 15 randomly selected cigarettes. Here’s the list of nicotine content values:

1.8, 1.4, 1.2, 1.3, 1.3, 1.8, 1.5, 0.8, 1.2, 1.7, 1.4, 1.4, 1.5

To check if this data follows an approximately normal distribution, we typically use statistical methods such as:

1. Shapiro-Wilk Test for Normality (for small sample sizes like this one),
2. Histogram or Q-Q Plot (visual assessment).

I'll perform the Shapiro-Wilk test for normality and provide the P-value. scipy.stats as stats

Data from the image

data = [1.8, 1.4, 1.2, 1.3, 1.3, 1.8, 1.5, 0.8, 1.2, 1.7, 1.4, 1.4, 1.5]

Perform the Shapiro-Wilk test for normality

statistic, p_value = stats.shapiro(data)

Return the test statistic and p-value

statistic, p_valueThe Shapiro-Wilk test for normality gave the following results:

• Test Statistic: 0.935
• P-value: 0.400

Since the P-value is greater than the significance level of 0.05 (alpha = 0.05), we fail to reject the null hypothesis. This indicates that there is not enough evidence to suggest that the data significantly deviates from a normal distribution.

Would you like to move on to the next part of the problem? Let me know if you'd like further details or explanations.

Here are some follow-up questions for further understanding:

1. How do you interpret the P-value in hypothesis testing?
2. What are other tests you could use to check for normality?
3. How would you visualize the data to assess its distribution?
4. What are the implications of failing to reject the null hypothesis in this case?
5. What assumptions are required for using the Shapiro-Wilk test?

Tip: Always check the sample size when performing normality tests. Small sample sizes can sometimes make it harder to detect deviations from normality.