Quiz 5

For any distribution, what is the z-score corresponding to the mean?

0

A coffee shop relocates to Italy and wants to make sure that all lattes are consistent. They believe that each latte has an average of 4 oz of espresso. If this is not the case, they must increase or decrease the amount. A random sample of 25 lattes shows a mean of 4.6 oz of espresso and a standard deviation of .22 oz. Use alpha = .05 and run a one sample t-test to compare with the known population mean.

13.6 > 2.064 ; Reject Ho

A researcher is testing the effect of a new cold and flu medication on mental alertness. A sample of n = 9 college students is obtained and each student is given the normal dose of the medicine. Thirty minutes later, each student's performance is measured on a video game that requires careful attention and quick decision making. The scores for the nine students are as follows: 6, 8, 10, 6, 7, 13, 5, 5, 3. Calculate the standard deviation. Is the data sufficient to conclude that the medication has a significant effect on mental performance? Test at the .05 level of significance.

3/ reject the null hypothesis

A researcher conducts a hypothesis test using a sample of n = 40 from an unknown population. What is the df value for the t statistic?

39

If two samples are selected from the same population, under what circumstances will the two samples have exactly the same t statistic?

If the samples are the same size and have the same mean and have the same variance.

Historically, evening long-distance calls from a particular city have averaged 15.2 minutes per call. In a random sample of 35 calls, the sample mean time was 14.3 minutes. Assume the standard deviation is known to be 5 minutes. Using a 0.05 level of significance, is there sufficient evidence to conclude that the average evening long-distance call has decreased?

T-test/Fail to reject the Null Hypothesis

If a researcher is using a t statistic to test a null hypothesis about a population, what information is needed from the population to calculate the t statistic?

The t statistic does not require any information about the population

Which of the following is a fundamental difference between the t statistic and a z-score?

The t statistic uses the sample variance in place of the population variance.

A population of scores with µ = 73 and σ = 20 is standardized to create a new population with µ = 50 and σ = 10. What is the new value for each of the following scores from the original population? Scores: 63, 65, 77, 83.

X = 63 / z = -0.50 / X = 45 ; X = 65 / z = -0.40 / X = 46 ; X = 77 / z = +0.20 / X = 52 ; X = 83 / z = +0.50/ X = 55

Significance level is also known as a______________.

alpha level

A ____ is a range of values that estimate the unknown population mean by estimating the t-value.

confidence interval

______ is a statement based upon the null hypothesis. It is either "reject the null hypothesis" or "fail to reject the null hypothesis".

decision

The number of independent pieces of information that go into the estimate of a parameter is called the _______________.

degrees of freedom

Which of the following describes what a confidence interval does?

it uses a sample mean to estimate the corresponding population mean.

The _______________ is a tentative explanation based on observations you have made

null hypothesis

If the retrieved t-value of -2.44 is smaller than the critical value of -2.093, the null hypothesis must be ___________

rejected

Whenever a sample is obtained from a population you expect to find some discrepancy between the sample mean and the population mean. This is called ______

sampling error

________________ is a statistical test to compare our sample populations and determine if there is a significant difference between their means.

t test

Any individual with a positive z-score has a score greater than the mean.

true

Transforming an entire distribution of scores into z-scores will not change the shape of the distribution.

true

When the population variance or standard deviation is not known, you must use a t statistic instead of a z‑score for a hypothesis test.

true

______ is supporting the alternative hypothesis when the null hypothesis is true.

type I error

Which of the following z-score values represents the location closest to the mean?

z= +.50