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 is definitely between 390 and 430.

The usual 95% confidence interval for  based on a sample of size n is 410    20. true or false …..?.  is definitely between 390 and 430. The statement is false. It’s quite plausible that μ is in this interval, but there is no guarantee.

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 is definitely between 390 and 430.

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  1. The usual 95% confidence interval for  based on a sample of size n is 410  20. trueor false…..?  is definitely between 390 and 430. The statement is false. It’s quite plausible that μ is in this interval, but there is no guarantee.

  2. The usual 95% confidence interval for  based on a sample of size n is 410  20. trueor false…..? is definitely between 390 and 430. The statement is true. After all, = 410.

  3. The usual 95% confidence interval for  based on a sample of size n is 410  20. trueor false…..? The probability is 95% that  is between 390 and 430. The statement is false. The probability that  can be between any two specified numbers must be either 0 or 1.

  4. The usual 95% confidence interval for  based on a sample of size n is 410  20. trueor false…..? The probability is 95% that is in the 95% confidence interval. This is false. As is always at the center of the interval, the probability must be 1.

  5. The usual 95% confidence interval for  based on a sample of size n is 410  20. trueor false…..? The population standard deviation  certainly exceeds 20. The statement is false; we have no way to make guarantees about σ. Also, 20 = and we have not been given the value of n.

  6. The usual 95% confidence interval for  based on a sample of size n is 410  20. trueor false…..? If you knew the value of , then you would have a shorter confidence interval. The statement is false. The length of the standard confidence interval depends on the random s, so there is no guarantee about which interval would be longer or shorter.

  7. The usual 95% confidence interval for  based on a sample of size n is 410  20. trueor false…..? The 99% confidence interval with the same data would be longer. The statement is true.

  8. The usual 95% confidence interval for  based on a sample of size n is 410  20. trueor false…..? The tdistribution was used in constructing this interval. The statement is true. The usual interval involves the t table. If the interval was provided by software, the t distribution was used implicitly.

  9. The usual 95% confidence interval for  based on a sample of size n is 410  20. trueor false…..? If we took a new sample of the same size, the probability is 0.95 that (the new mean) would fall between 390 and 430. The statement is false. It’s certainly intriguing. In fact, the probability is much larger than 95%.

  10. Can this happen …or is it impossible? Jason obtained a 95% confidence interval for the weight gain in ounces of laboratory mice that was longer than a 99% confidence interval for the weights in ounces of Granny’s snack cookies. Of course this can happen! These are separate problems.

  11. Can this happen …or is it impossible? LuAnn’s work on Friday involved the computation of 100 independent 95% confidence intervals, and it happened that seven of them failed to cover the target population parameters. Yes, this can happen. The expected number of non-coverage cases is five, but getting seven is very plausible.

  12. Can this happen … or is it impossible ? The standard binomial confidence interval can sometimes have a left end that is below zero. Yes, this can happen. The story with = 0 is not interesting. Consider = . The interval becomes and the left end can certainly be negative.

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