Statistics

Scenario 2: A random sample of 100 people was taken. Eighty-five of the people in the sample favored Candidate A. We are interested in determining whether or not the proportion of the population in favor of Candidate A is significantly more than 80%. What is the test statistic, the p value, and At 95% confidence, it can be concluded that the proportion of the population in favor of candidate A is...

1.25, 0.1056, is not significantly greater than 80%

The following data was collected from a simple random sample of a population: 13 15 14 16 12 What is the point estimate of pop mean, point estimate of standard deviation?

14, 1.581

The following information was collected from a simple random sample of a population. 16 19 18 17 20 18 What is the point estimate of the mean of the pop, and the point estimate of pop standard deviation?

18.0, 1.414

Scenario 1: Regression analysis was applied between sales data (Y) and advertising data (x) and the following information was obtained. ̂ = 12 + 1.8 𝑥 𝑌 n = 17 SSR = 225 SSE = 75 Sb1 = 0.2683 What is the f statistic, the critical f value of slope at 95% confidence, and the t statistic for testing the slope?

45, 4.54, 6.708

When the level of confidence increases, the confidence interval _____. a. stays the same b. becomes wider c. becomes narrower d. cannot be determined from the information given

B. Becomes wider

What type of error occurs if you fail to reject H0 when, in fact, it is not true? a. Type II b. Type I c. either Type I or Type II, depending on the level of significance d. either Type I or Type II, depending on whether the test is one tail or two tail

Type II

The weight of an object is an example of a. a continuous random variable b. a discrete random variable c. either a continuous or a discrete random variable, depending on the weight of the object d. either a continuous or a discrete random variable depending on the units of measurement

a continuous random variable

As the test statistic becomes larger, the p-value a. gets smaller b. becomes larger c. stays the same, since the sample size has not been changed d. becomes negative

a. gets smaller

In order to test the following hypotheses at an α level of significance H0: μ ≤ 800 Ha: μ > 800 the null hypothesis will be rejected if the test statistic Z is a. ≥ Zα b. < Zα c. < -Zα d. = Zα

a. ≥ Zα

If the coefficient of determination is 0.9, the percentage of variation in the dependent variable explained by the variation in the independent variable is a. 0.90% b. 90% c. 0.10% d. 10%

b. 90%

The number of customers who enter a store during one day is an example of _____. a. a continuous random variable b. a discrete random variable c. either a continuous or a discrete random variable, depending on the number of the customers d. either a continuous or a discrete random variable, depending on the gender of the customers

b. a discrete random variable

The level of significance in hypothesis testing is the probability of a. accepting a true null hypothesis b. accepting a false null hypothesis c. rejecting a true null hypothesis d. None of the above is correct.

c. rejecting a true null hypothesis

As the sample size increases, the _____. a. standard deviation of the population decreases b. population mean increases c. standard error of the mean decreases d. standard error of the mean increases

c. standard error of the mean decreases

The mean of a standard normal probability distribution _____. a. is always equal to 1 b. can be any value as long as it is positive c. can be any value d. None of the answers is correct.

d. None of the answers is correct.

A simple random sample of size n from a finite population of size N is a sample selected such that a. N has the same probability of being selected each possible sample of size _____. b. n has a probability of .5 of being selected c. n has a probability of .1 of being selected d. n has the same probability of being selected

d. n has the same probability of being selected

A sample of 24 observations is taken from a population that has 150 elements. The sampling distribution of 𝑥̅ is: a. approximately normal because 𝑥̅ is always approximately normally distributed b. approximately normal because the sample size is large in comparison to the population size c. approximately normal because of the central limit theorem d. normal if the population is normally distributed

d. normal if the population is normally distributed

A single numerical value used as an estimate of a population parameter is known as a_____. a. sample parameter b. population parameter c. point estimator d. point estimate

d. point estimate

A numerical description of the outcome of an experiment is called a _____. a. descriptive statistic b. probability function c. variance d. random variable

d. random variable

From a population that is normally distributed, a sample of 25 elements is selected and the standard deviation of the sample is computed. For the interval estimation of population mean, the proper distribution to use is the a. normal distribution b. t distribution with 25 degrees of freedom c. t distribution with 26 degrees of freedom d. t distribution with 24 degrees of freedom

d. t distribution with 24 degrees of freedom

As the sample size increases, the standard deviation of the sample means: a. increases b. decreases c. remains the same d. depends upon the specific population being sampled

decreases

A continuous probability distribution that is useful in describing the time, or space, between occurrences of an event is a(n) a. normal probability distribution b. uniform probability distribution c. exponential probability distribution d. Poisson probability distribution

exponential probability distribution

Which of the following is a required condition for a discrete probability function? a. ∑f(x) = 0 for all values of x b. f(x) 1 for all values of x c. f(x) < 0 for all values of x d. f(x) ≥0 for all values of x

f(x) ≥0 for all values of x

The probability that a continuous random variable takes any specific value: a. is equal to zero b. is at least 0.5 c. depends on the probability density function d. is very close to 1.0

is equal to zero

Which of the following is not a property of a binomial experiment? a. the experiment consists of a sequence of n identical trials b. each outcome can be referred to as a success or a failure c. the probabilities of the two outcomes can change from one trial to the next d. the trials are independent

the probabilities of the two outcomes can change from one trial to the next

The key difference between the binomial and hypergeometric distribution is that with the hypergeometric distribution is: a. the probability of success must be less than 0.5 b. the probability of success changes from trial to trail. c. the trails are independent of each other. d. the random variable is continuous.

the probability of success changes from trial to trail.

A uniform probability distribution is a continuous probability distribution where the probability that the random variable assumes a value in any interval of equal length is a. different for each interval. b. the same for each interval. c. at least one. d. None of these alternative is correct.

the same for each interval.

If two variables, x and y, have a strong linear relationship, then a. there may or may not be any causal relationship between x and y b. x causes y to happen c. y causes x to happen d. None of the above is correct.

there may or may not be any causal relationship between x and y

Scenario 3: The sales of a grocery store had an average of $8,000 per day. The store introduced several advertising campaigns in order to increase sales. To determine whether or not the advertising campaigns have been effective in increasing sales, a sample of 64 days of sales was selected. It was found that the average was $8,300 per day. From past information, it is known that the standard deviation of the population is $1,200. What is the null hypothesis, value of the test statistic, and the p value?

u >_ 8000, 2.0, 0.0228

Larger values of the standard deviation result in a normal curve that is a. shifted to the right b. shifted to the left c. narrower and more peaked d. wider and flatter

wider and flatter

If there is a very strong correlation between two variables then the coefficient of determination must be a. much larger than 1, if the correlation is positive b. much smaller than -1, if the correlation is negative c. any value larger than 1 d. None of the above is correct.

None of the above is correct.

When dealing with the number of occurrences of an event over a specified interval of time or space, the appropriate probability distribution is a: a. binomial distribution b. Poisson distribution c. uniform distribution d. hypergeometric probability distribution

Poisson distribution

In regression analysis, which of the following is not a required assumption about the error term ε? a. The expected value of the error term is one. b. The variance of the error term is the same for all values of X. c. The values of the error term are independent. d. The error term is normally distributed.

The expected value of the error term is one.

Which of the following is not a characteristic of the normal probability distribution? a. The mean, median, and the mode are equal b. The mean of the distribution can be negative, zero, or positive c. The distribution is symmetrical d. The standard deviation must be 1

The standard deviation must be 1