Question 1

Consider a significance test for a null hypothesis versus a two-sided alternative with a z-test statistic.Give a value of z that will give a result significant at the 1% level but not at the 5% level.
A) z = 1.96
B) z = -2.57
C) z = 3.98
D) There is no such z-value.

Accepted Answer

A z-value that is significant at the 1% level must be greater than approximately ±2.576 or less than -2.576, and any such value would also be significant at the 5% level. Therefore, there is no z-value that is significant at the 1% level but not at the 5% level.

Question 2

The mean amount of time needed to thaw a particular frozen dinner in the microwave prior to convection cooking is claimed to be 5.5 min, with standard deviation of 0.95 min.To test if the actual thaw time is longer than this, we sample 35 frozen dinners and record the amount of time to thaw each one.The average thaw time is 5.8 min.What is the p-value from this test?
A) 0.3761
B) 0.6239
C) 0.9693
D) 0.0307

Accepted Answer

We need to conduct a one-sample t-test, where:

Null hypothesis: The true mean thaw time is 5.5 min.
Alternative hypothesis: The true mean thaw time is greater than 5.5 min.

The test statistic is given by:
t = (sample mean - hypothesized mean) / (standard deviation / sqrt(sample size))
Plugging in the values:
t = (5.8 - 5.5) / (0.95 / sqrt(35)) = 1.72

The degrees of freedom = sample size - 1 = 34
Using a t-table or calculator, the p-value is found to be approximately 0.0307.
Since the p-value is less than the significance level of 0.05, we reject the null hypothesis and conclude that there is sufficient evidence to suggest that the true mean thaw time is longer than 5.5 min.

Question 3

The _______________ represents a significant difference from the current standard or existing state.
A) null hypothesis
B) alternative hypothesis
C) test statistic
D) true hypothesis

Accepted Answer

The alternative hypothesis is the one that proposes there is a significant difference or effect in comparison to the current standard or state. Option A (null hypothesis) represents no significant difference or effect, option C (test statistic) is a numerical value that helps us determine the likelihood of rejecting the null hypothesis, and option D (true hypothesis) is not a commonly used term in hypothesis testing.

Question 4

Psychologists wish to evaluate the consistency of a standardized behavioral test.The test is designed to have a variance of 225.Twenty randomly sampled tests yield a variance of 240.Assuming the underlying population is normal, test whether the actual population variance of this test appears to be significantly greater than its designed variance.State the critical value (CV), test statistic (TS), and conclusion from the test.(Use α = 0.01.)
A) CV = 27.2036; TS = 20.267; fail to reject H₀
B) CV = 36.1909; TS = 18.377; fail to reject H₀
C) CV = 36.1909; TS = 20.267; fail to reject H₀
D) CV = 27.2036; TS = 17.8125; reject H₀

Accepted Answer

The correct test for this scenario is the chi-square test for variance. The test statistic (TS) is calculated using the formula TS = (n-1)*s^2/σ^2, where n is the sample size, s^2 is the sample variance, and σ^2 is the population variance. Here, TS = (20-1)*240/225 = 20.267. The critical value (CV) for a chi-square test with df = n-1 = 19 at α = 0.01 (right-tailed test) is approximately 36.1909. Since TS < CV, we fail to reject the null hypothesis, indicating that the actual population variance does not appear to be significantly greater than its designed variance.

Question 5

Suppose you wish to investigate whether your spun tennis racquet is equally likely to land with the label facing up.Which of the following will always be true about the p-value in this situation?
A) The p-value will increase as the sample proportion that lands "up" increases.
B) The p-value will decrease as the sample proportion that lands "up" increases.
C) The p-value will increase as the sample proportion that lands "up" gets further from 0.5.
D) The p-value will decrease as the sample proportion that lands "up" gets further from 0.5.

Accepted Answer

The p-value is the probability of observing a sample proportion as extreme or more extreme than the one observed, assuming the null hypothesis is true. In this case, the null hypothesis is that the racquet is equally likely to land with the label facing up or down, so the p-value is the probability of observing a sample proportion that is as far from 0.5 as the one observed or further. As the sample proportion gets further from 0.5, the p-value will decrease.

Quiz 10: Hypothesis Tests Based on a Single Sample

Consider a significance test for a null hypothesis versus a two-sided alternative with a z-test statistic.Give a value of z that will give a result significant at the 1% level but not at the 5% level.

The _______________ represents a significant difference from the current standard or existing state.

Suppose you wish to investigate whether your spun tennis racquet is equally likely to land with the label facing up.Which of the following will always be true about the p-value in this situation?