Can someone provide comprehensive, step-by-step assistance for my Statistics homework on Quantitative methods I'm specifically seeking a solution that will help me understand the concepts better. Thank you in advance?

Answer 1

Of course! I'd be happy to help you with your Statistics homework and provide a step-by-step solution to enhance your understanding of the concepts. Here is the sample question with the solution.

Question:

A pharmaceutical company is conducting a study to evaluate the effectiveness of a new drug in reducing blood pressure. The company randomly selects 100 patients with hypertension and divides them into two groups: a treatment group receiving the new drug and a control group receiving a placebo. After 12 weeks, the systolic blood pressure measurements (mmHg) for each patient are recorded. The data collected for the treatment group are as follows:

Treatment Group (new drug):

Mean systolic blood pressure = 128

Standard deviation = 10

The data collected for the control group (placebo) are as follows:

Control Group (placebo):

Mean systolic blood pressure = 136

Standard deviation = 12

Using appropriate statistical techniques, determine whether there is a significant difference in the mean systolic blood pressure between the treatment and control groups. Assume a significance level of 0.05.

Solution:

To determine whether there is a significant difference in the mean systolic blood pressure between the treatment and control groups, we can perform an independent samples t-test.

Step 1: State the hypotheses:

Null hypothesis (H0): The mean systolic blood pressure in the treatment group is equal to the mean systolic blood pressure in the control group.

Alternative hypothesis (Ha): The mean systolic blood pressure in the treatment group is not equal to the mean systolic blood pressure in the control group.

Step 2: Set the significance level:

The significance level (α) is given as 0.05.

Step 3: Compute the test statistic:

We can use the two-sample independent t-test formula to calculate the test statistic:

t = (mean1 - mean2) / sqrt[(s1^2 / n1) + (s2^2 / n2)]

where:

mean1 = mean systolic blood pressure in the treatment group

mean2 = mean systolic blood pressure in the control group

s1 = standard deviation of systolic blood pressure in the treatment group

s2 = standard deviation of systolic blood pressure in the control group

n1 = sample size of the treatment group

n2 = sample size of the control group

Plugging in the given values, we have:

mean1 = 128, mean2 = 136, s1 = 10, s2 = 12, n1 = 100, n2 = 100

t = (128 - 136) / sqrt[(10^2 / 100) + (12^2 / 100)]

= -8 / sqrt[1 + 1.44]

= -8 / sqrt(2.44)

≈ -8 / 1.56

≈ -5.13

Step 4: Determine the critical value:

Since the test is a two-tailed test and the significance level is 0.05, we need to find the critical value corresponding to a significance level of 0.025 in each tail. From the t-distribution table or statistical software, the critical value for a two-tailed test with a degree of freedom (df) of 198 (n1 + n2 - 2) is approximately ±1.972.

Step 5: Make a decision:

Since the absolute value of the test statistic (-5.13) is greater than the critical value (1.972), we reject the null hypothesis.

Step 6: State the conclusion:

There is sufficient evidence to conclude that there is a significant difference in the mean systolic blood pressure between the treatment and control groups (p < 0.05). The new drug appears to have a significant effect on reducing blood pressure compared to the placebo.

If you require assistance with statistics homework or any other statistical analysis, feel free to reach out. As an expert in statistics, I am here to help you navigate the complexities of quantitative methods and ensure a comprehensive understanding of statistical concepts and their applications.

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