Week 1
Assuming a normal distribution, as the standard deviation increases, the shape of curve
Becomes shorter and wider
For a confidence level of 94%, find the Z-critical value
1.88
The claim that is assumed to be true in a hypothesis test is called
The Null Hypothesis
You are performing a right-tailed t-test with a sample size of 15
If α=.005α=.005, and your test statistic is t=2.25t=2.25, do you:
Fail to Reject Null Hypothesis
All else equal, an increase in the level of confidence will cause a(n) _____ in the size of a confidence interval.
Increase
As the standard deviation of a normal curve decreases, the data becomes __________ centered around the mean.
More
All else equal, an increase in sample size will cause a(n) _____ in the size of a confidence interval.
Decrease
Food inspectors inspect samples of food products to see if they are safe. This can be thought of as a hypothesis test with the following hypotheses. However, The sample suggests that the food is safe, but it actually is not safe. What type of error is this?
Type II
You are performing a right-tailed z-test
If α=.01α=.01, and your test statistic is z=2.29z=2.29, do you:
Fail to Reject Null Hypothesis
Test the claim that the proportion of people who own cats is larger than 30% at the 0.05 significance level.
H0:p≤0.3
H1:p>0.3
When sampling and the standard deviation is not known, what is used to estimate it?
The standard deviation of the data from the sample
Why does sample size need to be accounted for in the t-distribution?
The t-distribution changes for different sample sizes
Which of the following represents the probability of correctly rejecting an invalid null hypothesis?
The Power of the Test
Given the sample mean = 22, sample standard deviation = 3.7893, and N = 40 for the low income group,
Test the claim that the mean nickel diameter drawn by children in the low income group is greater than 21.21 mm. Test at the 0.1 significance level.
Identify the correct alternative hypothesis
μ>21.21
The following formulas would you use to compute a critical value for a 95% level of confidence to estimate the population mean given an assumed standard deviation of 10 and a sample size of 35,
=NORMSINV(0.025)
GPAs at CCSU are normally distributed with a mean of 2.45 and a standard deviation of 0.51. Find the zz-score for a GPA of 3.21.
1.490
SAT scores are distributed with a mean of 1,500 and a standard deviation of 300. You are interested in estimating the average SAT score of first year students at your college. If you would like to limit the margin of error of your 95% confidence interval to 25 points, how many students should you sample?
554
The p-value for a hypothesis test turns out to be 0.04753. At a 9% level of significance, what is the proper decision?
Reject H0
H0:μ=13.13H0:μ=13.13
H1:μ>13.13H1:μ>13.13
Your sample consists of 37 subjects, with a mean of 13.6 and a sample standard deviation (s) of 1.54. Calculate the Test Statistic.
1.86
You are performing a right-tailed z-test
If α=.025α=.025, and your test statistic is z=2.91z=2.91, do you:
Reject Null Hypothesis
According to the Empirical Rule, 95% of the area under the normal curve is within two standard deviations of the mean. What percent of the area under the normal curve is more than two standard deviations from the mean?
5%
The following formulas would you use to compute a critical value for a 92% level of confidence to estimate the population mean given a sample standard deviation of 10 and a sample size of 35,
=T.INV.2T(0.08,34)
Failing to reject an invalid null hypothesis (continuing to incorrectly assume a null is valid) is called:
The Beta-Risk
You are performing a two-tailed test.
If α=.08α=.08, find the positive critical value, to three decimal places.
1.751
You are performing a right-tailed test.
If α=.02α=.02, find the critical value, to three decimal places.
2.054