Statistical Analysis Summary and Inferences from Questions 6 to 10 in Data Analysis

Question 6.

1. Based on the Levene’s test, we cannot assume equal variances since we have p = 0.0014
   2. The test statistic is -2.0370.

We are 95% confident that the true difference in average number of items bought online between the two groups, Group A and Group B, lies within the interval (-6.4183, -0.0682).

Since we have p = 0.0454, we can reject H0 and therefore conclude that the difference in average number of items bought online between the two groups is statistically significant. Further supporting this conclusion is the fact that the confidence interval does not contain zero.

[5:29 am, 10/11/2023] Vaidehi Iyer: Question 7.
1. The sample correlation coefficient is r = -0.8276. This tells us that the association between the two variables is strong and negative.

2. We are 95% confident that the true correlation between x and y is between -0.8808 and -0.7537.
3. The p-value is equal to 0. Therefore, there is evidence of a significant association between the two variables.
4. Plot B
   5. a. The slope of the blue line in the above graph must be -6.
5. Y can be found out as:

y = 35 - 6(2) = 35 - 12 = 23
so, y = 23
[5:39 am, 10/11/2023] Vaidehi Iyer: Question 8.

1. Given that the expected number of successes is less than 10, the conditions for the one-sample test of proportions are not fully met.
2. The estimate for p is p^ = 0.0980 (rounded to four decimal places). We are 95% confident that the true proportion of left-handed people in the population is between 0.0367 and 0.2219.
3. The p-value is equal to 0.2103. Therefore, we cannot reject H0. Further supporting this conclusion is the fact that the 95% confidence interval does include 0.05.

[5:50 am, 10/11/2023] Vaidehi Iyer: Question 9.

1. In this case, we have 60 mothers in each group, which satisfies the sample size condition. In the control group, there were 8 premature births and 52 full-term births. In the intervention group, there were 6 premature births and 54 full-term births. Therefore, both groups have at least 10 successes and 10 failures. so, all the conditions for the two-sample test of proportion have been met.
2. The estimate for p1 is 0.1333. We are 95% confident that the difference in proportion between groups is within the interval [-0.0981, 0.1647].
3. The p-value is equal to 0.7761. Therefore, we fail to reject H0. Further supporting this conclusion is the fact that the 95% confidence interval includes zero.
   [5:58 am, 10/11/2023] Vaidehi Iyer: Question 10.
4. The test statistic is equal to 15.013.
   3. The degrees of freedom is equal to 3.
5. The p-value is equal to 0.0018. Therefore, we reject H0. This means that there is sufficient evidence to support that the distribution of proportions is significantly different from what was expected.
   [6:00 am, 10/11/2023] Vaidehi Iyer: Question 10.
6. df = (3 - 1) * (2 - 1) = 2

So the degrees of freedom for this study is 2.

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