When should the Student t distribution be used in constructing a confidence interval for the population mean?

You must use the t-distribution table when working problems when the population standard deviation (σ) is not known and the sample size is small (n<30). General Correct Rule: If σ is not known, then using t-distribution is correct.

What is the confidence interval for t distribution?

By replacing the normal distribution with the t-distribution we really do have 95\% confidence that the interval contains the mean.

What happens to confidence interval as sample size increases?

Increasing the sample size decreases the width of confidence intervals, because it decreases the standard error. 95\% confidence means that we used a procedure that works 95\% of the time to get this interval.

When constructing a confidence interval as the confidence level required in estimating the mean increases the width of the confidence interval?

The width of the confidence interval decreases as the sample size increases. The width increases as the standard deviation increases. The width increases as the confidence level increases (0.5 towards 0.99999 – stronger).

When constructing the confidence interval for a mean why do we use a t distribution and how does it differ from a normal distribution?

The reason t-distribution is used in inference instead of normal is due to the fact that the theoretical distribution of some estimators is normal (Gaussian) only when the standard deviation is known, and when it is unknown the theoretical distribution is Student t. We rarely know the standard deviation.

What are the conditions for constructing a confidence interval?

When constructing confidence intervals the assumptions and conditions of the central limit theorem must be met in order to use the normal model. Randomization Condition: The data must be sampled randomly. Sample Size Condition: The sample size must be sufficiently large.

How does the T distribution compare with the normal distribution?

The T distribution is similar to the normal distribution, just with fatter tails. Both assume a normally distributed population. T distributions have higher kurtosis than normal distributions. The probability of getting values very far from the mean is larger with a T distribution than a normal distribution.

Why does the confidence interval get wider as the confidence level increases?

Correct answer: Larger samples give narrower intervals. We are able to estimate a population proportion more precisely with a larger sample size. A larger confidence level increases the chance that the correct value will be found in the confidence interval. This means that the interval is larger.

What happens to confidence interval as sample size decreases?

If we decrease the sample size n to 25, we increase the error bound. Increasing the sample size causes the error bound to decrease, making the confidence interval narrower. Decreasing the sample size causes the error bound to increase, making the confidence interval wider.

How does confidence level affect confidence interval?

As the confidence level increases the width of the confidence interval also increases. A larger confidence level increases the chance that the correct value will be found in the confidence interval. This means that the interval is larger.

What happens to the confidence interval when you decrease the confidence level and why?

Increasing the confidence level increases the error bound, making the confidence interval wider. Decreasing the confidence level decreases the error bound, making the confidence interval narrower.

What is the importance of confidence intervals?

Why are confidence intervals important? Because confidence intervals represent the range of scores that are likely if we were to repeat the survey, they are important to consider when generalizing results.

What is confidence interval in statistics?

Every Confidence interval has an associated Confidence Level: • Confidence interval in Statistics is a type of range estimate for a population parameter based on one or more samples. For instance if we want to estimate the average height of all teenage USA boys aged 15 from a sample of one hundred 15 years old teens.

How does increasing the sample size affect the width of confidence intervals?

Increasing the sample size decreases the width of confidence intervals, because it decreases the standard error. c) The statement, “the 95\% confidence interval for the population mean is (350, 400)”, is equivalent to the statement, “there is a 95\% probability that the population mean is between 350 and 400”.

What does 95\% confidence mean in statistics?

False. 95\% confidence means that we used a procedure that works 95\% of the time to get this interval. That is, 95\% of all intervalsproduced by the procedure will contain their corresponding parameters. For any one particular interval, the true population percentage is either inside the interval or outside the interval.

Why does my 95\% confidence interval reject my null hypothesis?

If the 95\% confidence interval does not contain the hypothesize parameter, then a hypothesis test at the 0.05 α level will almost always reject the null hypothesis. This example uses the Body Temperature dataset built in to StatKey for constructing a bootstrap confidence interval and conducting a randomization test .