The Mean BMI In Patients Free Of Diabetes Was Reported As 28

The Mean Bmi In Patients Free Of Diabetes Was Reported As 282 The In

The mean BMI in patients free of diabetes was reported as 28.2. The investigator conducting the study hypothesizes that the BMI in patients free of diabetes is higher. Based on the data given below, is there evidence that the BMI is significantly higher than 28.2? Use a 5% level of significance. Critical t value: (2 points) Computed t = (2 points) Based on comparing the critical t value to the computed t value, which of the following is (are) true? a. There is statistically significant evidence at alpha=0.05 to show the BMI is significantly higher than 28.2. b. There is not statistically significant evidence at alpha=0.05 to show the BMI is significantly higher than 28.2. c. There are not enough data points to reach a conclusion. d. b and c.

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The Mean Bmi In Patients Free Of Diabetes Was Reported As 282 The In

The provided question involves performing a hypothesis test to determine whether the mean Body Mass Index (BMI) in patients free of diabetes is significantly higher than a specified value. The reported mean BMI is 28.2, and the researcher hypothesizes that the true mean BMI exceeds this value. To assess this, a one-sample t-test for the mean is appropriate, considering the significance level of 5%.

Understanding the Hypotheses

The null hypothesis (H₀) states that the population mean BMI equals 28.2, written as:

• H₀: μ = 28.2

The alternative hypothesis (H₁) posits that the population mean BMI is greater than 28.2, expressed as:

• H₁: μ > 28.2

This is a one-tailed test focusing on the upper tail of the distribution because the hypothesis concerns whether the mean BMI is higher than the specified value.

Data and Computations Needed

To conduct the hypothesis test, we need the sample data, specifically:

• The sample mean (given as 28.2, which may be from the data)
• The sample standard deviation (s)
• The sample size (n)

With these, we can compute the test statistic (t) using the formula:

t = (x̄ - μ₀) / (s / √n)

where x̄ is the sample mean, μ₀ is the hypothesized mean (28.2), s is the sample standard deviation, and n is the sample size.

Critical Value and Decision Criteria

At a significance level of 0.05 and with degrees of freedom df = n - 1, the critical t value is obtained from the t-distribution table. For a one-tailed test, if the computed t exceeds the critical t value, we reject H₀.

Interpretation of Results

Since the problem states a computed t value and a critical t value (though unspecified), the decision rules are:

• If computed t > critical t, reject H₀: evidence suggests the mean BMI is higher than 28.2.
• If computed t ≤ critical t, do not reject H₀: insufficient evidence to support the hypothesis that the mean BMI exceeds 28.2.

Conclusion Based on Given Options

The multiple-choice options are:

1. There is statistically significant evidence at alpha=0.05 to show the BMI is significantly higher than 28.2.
2. There is not statistically significant evidence at alpha=0.05 to show the BMI is significantly higher than 28.2.
3. There are not enough data points to reach a conclusion.
4. b and c.

Given the typical interpretation of hypothesis testing, the correct conclusion depends on the comparison of the critical t value with the computed t. If the computed t surpasses the critical t, then the answer is 'a.' Otherwise, the correct answer is 'b.' The options 'c' and 'd' imply insufficient data and overlapping possibilities, but without specific values, a definitive choice aligns with interpreting hypothesis test results as per standard procedures.

Final Remarks

Therefore, the process for the analysis involves calculating the t-statistic with actual data points. From the results, conclusions about the hypothesis can be made. As the question provides no explicit computed t value or sample size, the decision is contingent upon these values, but the procedure remains consistent: compare the computed t against the critical value and infer the conclusion accordingly.

References

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