Confidence Intervals and Hypothesis Testing

The video tutorial explains statistical inference using confidence intervals. It begins with an introduction to the concept, followed by an example using birth weights of Pittsburgh newborns. The tutorial details the construction of a 95% confidence interval and its interpretation, highlighting that the interval does not contain the assumed population mean. The significance of the p-value is discussed, emphasizing its role in statistical inference. Finally, the video explores a 99% confidence interval, demonstrating how it is wider and still does not include the assumed mean, reinforcing the conclusion that the sample mean is statistically different from the assumed population mean.

What is the assumed population mean for the birth weights of Pittsburgh newborns in the example?

• 6.5 pounds

• 7 pounds

• 7.5 pounds

• 6 pounds

What is the critical value used for constructing a 95% confidence interval?

• 1.64

• 2.33

• 1.96

• 2.58

What does a 95% confidence interval indicate about the true population mean?

• It is greater than the sample mean.

• It is exactly equal to the sample mean.

• It is less than the sample mean.

• It lies within the interval with 95% confidence.

What does a p-value of less than 0.001 suggest about the sample mean?

• It is likely from the assumed population mean.

• It is unlikely from the assumed population mean.

• It is irrelevant to the assumed population mean.

• It is exactly the assumed population mean.

How does the confidence interval change when moving from 95% to 99% confidence?

• It becomes narrower.

• It remains the same.

• It becomes wider.

• It becomes invalid.

What is the new range of the 99% confidence interval?

• 6.7 to 7.3

• 6.5 to 7.5

• 6.79 to 7.21

• 6.83 to 7.16

Why does the 99% confidence interval not contain the assumed population mean of 6.5?

• The sample mean is incorrect.

• The assumed population mean is incorrect.

• The interval is too narrow.

• The sample size is too small.

What inference can be made if the hypothesized true mean does not fall into the confidence interval?

• The sample mean is exactly the assumed mean.

• The sample mean is statistically similar to the assumed mean.

• The sample mean is statistically different from the assumed mean.

• The sample mean is irrelevant to the assumed mean.

What is the significance level when the sample mean is statistically different from the assumed mean at the 1% level?

• 10%

• 5%

• 0.1%

• 1%

What does the confidence interval and p-value together suggest about the sample mean?

• It is exactly the assumed population mean.

• It is likely from the assumed population mean.

• It is unlikely from the assumed population mean.

• It is irrelevant to the assumed population mean.