STATS

The probability of making a Type II error is denoted by

β.

A machine is designed to fill toothpaste tubes, on an average, with 5.8 ounces of toothpaste. The manufacturer does not want any underfilling or overfilling. The correct hypotheses to be tested are

H0: μ = 5.8 Ha: μ ≠ 5.8.

The average hourly wage of computer programmers with 2 years of experience has been $21.80. Because of high demand for computer programmers, it is believed there has been a significant increase in the average hourly wage of computer programmers. To test whether or not there has been an increase, the correct hypotheses to be tested are

H0: μ ≤ 21.80 Ha: μ > 21.80

As the sample size increases, the margin of error

becomes narrower

To compute the minimum sample size for an interval estimate of μ, we must first determine all of the following except

degrees of freedom

An estimate of a population parameter that provides an interval of values believed to contain the value of the parameter is known as the

interval estimate

If the null hypothesis is rejected at the 5% level of significance, it

may be rejected or not rejected at the 1% level

Sampling distribution of x̄ is the

probability distribution of the sample mea

The probability distribution of all possible values of the sample proportion p̄ is the

sampling distribution of p̄.

A two-tailed test is performed at the .05 level of significance. The p-value is determined to be .09. The null hypothesis

should not be rejected

As the sample size increases, the

standard error of the mean decreases.

When s is used to estimate σ, the margin of error is computed by using the

t distribution.

If the null hypothesis is rejected in hypothesis testing,

the alternative hypothesis is true

Which of the following does not need to be known in order to compute the p-value?

the level of significance

The probability of committing a Type I error when the null hypothesis is true as an equality is

the level of significance.

Check My Work The sum of the values of α and β

is not needed in hypothesis testing

What type of error occurs if you fail to reject H0 when, in fact, it is not true?

type 2

A simple random sample of 144 observations was taken from a large population. The sample mean and the standard deviation were determined to be 1234 and 120 respectively. The standard error of the mean is

10

The t value for a 95% confidence interval estimation with 24 degrees of freedom is

2.064

The t value for a 95% confidence interval estimation with 24 degrees of freedom is

2.064.

As the number of degrees of freedom for a t distribution increases, the difference between the t distribution and the standard normal distribution

Becomes smaller

The value added to and subtracted from a point estimate in order to develop an interval estimate of the population parameter is known as the

Margin of error

When s is used to estimate σ, the margin of error is computed by using the

T distrubution

A 95% confidence interval for a population mean is determined to be 100 to 120. For the same data, if the confidence coefficient is reduced to .90, the confidence interval for μ

becomes narrower.

As the number of degrees of freedom for a t distribution increases, the difference between the t distribution and the standard normal distribution

becomes smaller.

As the sample size increases, the margin of error

decreases

An estimate of a population parameter that provides an interval of values believed to contain the value of the parameter is known as the

interval estimate.

For a given confidence level and when σ is known, the margin of error in a confidence interval estimate

is the same for all samples of the same size

The value added to and subtracted from a point estimate in order to develop an interval estimate of the population parameter is known as the

margin of error.

For the interval estimation of μ when σ is known and the sample is large, the proper distribution to use is the

normal distribution.

Doubling the size of the sample will

reduce the standard error of the mean to approximately 70% of its current value.

From a population that is normally distributed, a sample of 25 elements is selected and the standard deviation of the sample is computed. For the interval estimation of μ, the proper distribution to use is the

t distribution with 24 degrees of freedom

In interval estimation, the t distribution is applicable only when

the sample standard deviation is used to estimate the population standard deviation.