Question 1

Whenever a sample is selected and measured, one must assume that the sample mean

Accepted Answer

It is unlikely for the sample mean to be identical to the population mean, as there is always some degree of sampling error present. Therefore, it is reasonable to assume that the sample mean will probably differ from the population mean.

Question 2

When an area (between high and low values) of the sampling distribution of means have been bracketed on the basis of a reasonable expectation of containing (estimating) the population mean, then

Accepted Answer

When an area (between high and low values) of the sampling distribution of means have been bracketed on the basis of a reasonable expectation of containing (estimating) the population mean, it is called a confidence interval. Therefore, the correct choice is D- the confidence interval has been calculated. The central limit theorem does not need to be proven as it is a proven mathematical theorem. A point estimate refers to a single value used to estimate the population mean rather than an interval. The alpha level refers to the level of significance chosen for hypothesis testing and is not relevant to calculating confidence intervals.

Question 3

Increasing the confidence-interval level from .95 to .

Accepted Answer

Increasing the confidence interval level from .95 to a higher level increases the margin of error and widens the interval. This increased width makes it more likely for the population mean to fall within the interval, increasing the likelihood of including the population mean within its limits.

Question 4

According to the text, the highest value that should be assigned to the alpha level is

Accepted Answer

The text states that the highest value that should be assigned to the alpha level is .05, which is commonly used as the standard level of significance in statistical hypothesis testing. It is important to choose a low alpha level to minimize the chance of making a Type I error (rejecting a true null hypothesis).

Question 5

Other things being equal, an alpha level of .05 should lead to a rejection of the null hypothesis

Accepted Answer

A lower alpha level means a stricter criteria for rejecting the null hypothesis. Therefore, an alpha level of .05 (compared to .10) should lead to a rejection of the null hypothesis more often. However, an alpha level of .01 is even stricter than .05, so the null hypothesis would be rejected less often than when alpha is set at .01.

Question 6

The single-sample t ratio is used to compare

Accepted Answer

The single-sample t ratio is used to compare a sample mean with an assumed or known population mean. It is used when the population standard deviation is not known and the sample size is small (less than 30).

Question 7

Other things being equal, the higher the value of the t ratio

Accepted Answer

The higher the value of the t ratio, the further the sample mean is from the null hypothesis and the more likely it is that the difference is statistically significant. This increases the likelihood of rejecting the null hypothesis.

Question 8

Rejecting Ho when in fact we should have failed to reject it, causes the

Accepted Answer

Rejecting Ho when it is actually true is known as a Type 1 error. It occurs when we falsely reject the null hypothesis and see a significant difference where there is none. This error can lead to false conclusions and incorrect decisions.

Question 9

When we fail to reject null hypothesis, then we know for certain that

Accepted Answer

Failing to reject the null hypothesis does not mean that we know for certain that the mean of the sample equals the mean of the population or that it differs from the mean of the population. It also does not mean that the mean of the sample is a biased estimator. The statistical decision is a probability statement and does not provide a certain answer.

Question 10

The fact that the point estimate of the population mean may be inaccurate (even with random sampling) is due largely to

Accepted Answer

The inaccuracy of the point estimate of the population mean, even with random sampling, is due to sampling error, which occurs naturally due to the variability in samples that are selected from a population. This means that the sample mean may not perfectly represent the true population mean. Bias refers to systematic errors in the sampling process, while alpha error pertains to errors made in hypothesis testing. The fourth option is incorrect, as the population mean can be estimated through statistical methods.

Question 11

A single-sample t ratio is only considered to be significant when

Accepted Answer

The single-sample t ratio is only considered to be significant when the null hypothesis has been rejected at a certain level of significance, typically α = 0.05. This means that there is strong evidence against the null hypothesis, and the sample results are unlikely to be due to chance alone.

Question 12

For the t ratio, the larger the sample size

Accepted Answer

The t ratio is calculated using the sample mean and standard deviation and is further influenced by the number of degrees of freedom. As the sample size increases, the degrees of freedom also increase, resulting in a smaller t value and a more precise test. Therefore, the larger the sample size, the larger the number of degrees of freedom.

Question 13

When the null hypothesis is rejected, then we know for certain that

Accepted Answer

The rejection of the null hypothesis only indicates that there is sufficient evidence to suggest that the null hypothesis is not true. However, it does not provide certainty as statistical decisions are based on probabilities. Therefore, none of the given options can be said to be certain.

Question 14

Estimating the value of the population mean on the basis of the sample mean alone produces a(n)

Accepted Answer

A point estimate is an estimate of a population parameter based on a sample statistic. In this case, using the sample mean as an estimate of the population mean is a point estimate.

Question 15

With a single-sample t ratio, the null hypothesis states that

Accepted Answer

The null hypothesis for a single-sample t test states that the sample mean is not significantly different from the population mean. This means that the sample mean could readily be part of the same distribution whose overall mean is already known.

Question 16

When a given difference is determined to be "significant", then

Accepted Answer

When a difference is determined to be "significant," it means that the null hypothesis (which assumes no difference exists) was rejected based on the results of the statistical significance test. Therefore, choice C is the correct answer. Choices A, B, and D are incorrect because they do not accurately reflect the meaning of a significant difference in statistical hypothesis testing.

Question 17

A single-sample t ratio presents the difference between two means in units of

Accepted Answer

The single-sample t ratio presents the difference between two means in units of the estimated standard error of the mean.

Question 18

If it is determined that there is no difference between the population mean being represented by the sample and the mean of the population at large, then

Accepted Answer

If there is no difference between the population mean being represented by the sample and the mean of the population at large, it means that the null hypothesis cannot be rejected. Therefore, the answer is D, which means there was a failure to reject the null hypothesis.

Question 19

The true population mean is expected to fall outside a .99 confidence interval

Accepted Answer

A 99% confidence interval means that there is a 1% chance that the true population mean falls outside of the interval. Therefore, choice A is correct. Choice B is incorrect because it suggests that the true mean falls within the confidence interval 99% of the time, which is not true. Choice C is incorrect because there is always some chance that the true population mean falls outside of the confidence interval, no matter how confident we are. Choice D is incorrect because although it is possible for the true mean to never fall outside the confidence interval, it is not always the case.

Question 20

A point estimate of a population value is referred to as

Accepted Answer

The answer of A point estimate of a population value...

Quiz 8: Parameter Estimates