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Determine if the following statements are true or false, and explain your reasoning. If false, state how it could be corrected. (a) If a given value (for example, the null hypothesized value of a parameter) is within a 95% confidence interval, it will also be within a 99% confidence interval. (b) Decreasing the significance level (↵) will increase the probability of making a Type 1 Error. (c) Suppose the null hypothesis is μ = 5 and we fail to reject H0. Under this scenario, the true population mean is 5. (d) If the alternative hypothesis is true, then the probability of making a Type 2 Error and the power of a test add up to 1. (e) With large sample sizes, even small differences between the null value and the true value of the parameter, a difference often called the effect size , will be identified as statistically significant.

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MrRoyal

Answer:

a. True

b. False

c. False

d. True

e. True

Step-by-step explanation:

a.

True,

A 99% confidence interval covers more than a 95% confidence interval.

This is because, more potential values must be allowed within the interval, to be more confident that the true population value falls within the interval

b.

False,

Decreasing the significance level will decrease the probability of making a type 1 error because the probability of a Type I error is the same as α.

c.

False,

The evidence is not sufficient to make a conclusion that µ = 5.

d. True

The probability of making a type II error (failing to reject the null hypothesis when it is actually false) is called β (beta).

The probability of not making this error is 1 - β

1 - β + β = 1

e.

True,

Large sample sizes can decrease the margin of error.

Because the relationship between margin of error and sample size is simple is that when the sample size increases, the margin of error decreases and vice versa

The correct option regarding the samples will be:

  • True
  • False
  • False
  • True
  • True

Sampling

It should be noted that a 99% confidence interval covers more than a 95% confidence interval. Therefore, it's true.

Also, the reduction of the significance level will also decrease the probability of making a type 1 error because the probability of a Type I error is the same as α.

The probability of making a type II error is called β. Therefore, it's true.

Lastly, large sample sizes can decrease the margin of error.

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