Stats Final

In a z-distribution, what is the relationship between a critical value and an unlikely event?

A critical value is a value of z that separates a likely outcome from an unlikely outcome.

What exactly is a "z-score" as far as a normal distribution is concerned?

A z-score is the number of standard deviations that a date value is away from the mean a population.

A coin is weighed so that it comes up heads 75% of the time. If you toss it ten times, what is the probability that you get exactly five heads?

.058

According to the empirical rule for normal distributions, which one of the following statements is true?

95% of the population data its will be found between +-2 standard deviations of the mean.

You are taking a sample size of 36 from a normally distributed population, mean of 50, standard deviation of 12. What is the probability that your sample will be between 46 and 54?

95.4%

Suppose you are running a test for a correlation and your computed r value is .75. If your sample size is n=7 at a level of significance 0.05, what will be your predicted value for x=17? (x=17, y=98, y=4x+10)

98

After conducting an ANOVA test we might conclude that there is sufficient evidence to reject a claim of equal means. If so, what method might be used to determine which population mean is different from the others?

Construct confidence interval estimates for the means of the different populations.

For a one way ANOVA test with a significance level of 0.05. If the sample means of different populations are X1=16,X2=16.2, X3=17, X4=15.9.And the p-value of the test is 0.03. Then what can you conclude.

Due to the p-value of 0.03 being less than the significance level of 0.05, we can conclude that there is sufficient evidence to reject the null hypothesis.

Suppose you have three items chosen from a normal distribution with z-scores of 2.1, 2.03, and 2.15. The distribution has a mean of 10.56 pounds and a standard deviation of 0.25 pounds. What do you know about the three items selected?

Each of the three items weighs more than 10.56 pounds.

What does it mean if you use a sample size 50 to construct a 95% Confidence interval for a population proportion?

If you construct 100 such intervals in the same manner, you would expect that 95 of the constructed intervals would contain the true population proportion.

In a test of hypothesis using the normal distribution, how does one find the p-value of the test?

In a one-sided test, the p-value is the area under the curve beyond the z-value given by the test statistic.

What is the "confidence interval method" of hypothesis testing?

In the confidence interval method you first calculate the test statistic and hen examine the confidence interval to see if it contains that value. If it does, you fail to reject the null hypothesis.

In hypothesis testing, what is the major difference between the p-value method and the critical value method?

In the p-value method the test statistic determines the p-value. In the critical value method the test statistic is compared to a pre-established critical value.

What is standard error?

It's the std dev of the sampling distribution of the sample means, which can be a normal or T.

In an experiment of tossing a biased coin 100 times, with p(H)=60% , calculate the probability of getting exactly 55 heads and the probability of getting more than 55 heads.

P(X=55)= .048 and P(X>55)= .821

Choose the set of measures in the answer where the measures are all equivalent.

Q2, the median and P50

What is the distinction between the "difference of the means" and the "mean of the differences?

The "difference of the means" refers to two independent means from two independent populations. The "mean of the differences" refers to a set of paired data where you first find the difference of each matched pair.

What is the meaning of the term "standard error"?

The "standard error" is the standard deviation of the sampling distribution.For example, the "standard error of the mean" is the standard deviation of the sampling distribution of sample means, sd/root n

ANOVA helps in determining whether the population mean in three or more populations are the same or not. If one rejects the null hypothesis: the equality of the means, then it suggests that at least one of the population mean is different from others. What method can be used to determine which population mean is different from the others?

The confidence interval for different populations gives an idea of their corresponding parameter, here it's mean. so constructing the CI for the populations and verifying which population mean is different.

What will be the impact on the graph of a normal distribution if there are a few low-end outliers?

The graph will be almost normal but skewed somewhat to the left

What is measured by the linear correlation coefficient, r?

The linear coefficient measures how well a sample of paired sample data fits a straight-line pattern.

You are writing an article about truck brand ownership among Detroit auto workers. your null hypothesis is that ownership preferences are evenly split among Ford, chevy, dodge, and toyota. After taking a sample of 100 trucks in the factory parking lot, with a level of significance 0.05 you get a test statistic of 15.598. What conclusion would you draw?

The ownership preferences are not evenly split.

Typically, a probability distribution of a population proportions consists of. finite number of possible proportions. So what then justifies the use of a continuous normal distribution when working on problems involving proportions?

The probability distribution will be close to normal if the requirements for a binomial distribution are met and np>_ and nq>_5.

Suppose you set up an experiment where you toss a fair coin 100 times. What is the probability that you will get exactly 49 heads? Is this a likely event or an unlikely event?

The probability of 49 heads is 7.8%. This number of heads would not be unusual.

Suppose you select a sample size of 10 from a population of paired data and you calculate a correlation coefficient r=.802. At a level of significance alpha= 0.01, what conclusion would you draw?

The sample data support the claim that there is correlation between the two variables.

If a sample of sample size 49 is taken from a normally distributed population, with mean=50 and sd=14. What is the probability that the mean of the sample will be between 45 and 55?

The sample is distributed as a normal distribution with mean=50, but the sd=14/7=2. Hence either from stratcrunch or converting it to z-scores, the p(45<X<55)= 0.988 or 98.76%

which of the following statements is true regarding a sampling distribution of sample means?

The standard deviation of the distribution is equal to the standard deviation of the population divided by the square-root of the sample size.

Consider a one way ANOVA test against four populations at a significance level of 0.05.The p-value of the test id 0.04. If the sample means were x1=14, x2=14.2, x3=15, x4= 13.9, what does the test tell us about whether or not one of these populations has a mean different from the others?

The test indicates that at least one of the populations has a mean different from the others, but we don't know which one.

What is one of the unique features of a probability histogram?

The total area of all the rectangles comprising the histogram much be 1.

Let's say that under a certain set of assumptions that the probability of event A occurring is less than 2%. Given that event A does occur, what can we say about the underlying assumption?

There is strong evidence that the assumptions were not correct.

In an ANOVA test for four different population each with sample size of 10, what is the associated distribution?

it's an F distribution with numerator df= 3 and denominator df=36

What is the mean of the sampling distribution of the sample proportions?

it's the same of the population proportion which is P.