# Probability, hypothesis testing and confidence intervals

What is an important similarity between the uniform and normal probability distributions?

A. The mean, median and mode are all equal.

B. The mean and median are equal.

C. They are negatively skewed.

D. About 68% of all observations are within one standard deviation of the mean.

The distribution of the annual incomes of a group of middle management employees approximated a normal distribution with a mean of $37,200 and a standard deviation of $800. About 68 percent of the incomes lie between what two incomes?

A. $30,000 and $40,000

B. $36,400 and $38,000

C. $34,800 and $39,600

D. $35,600 and $38,800

A marketing firm is studying consumer preferences for winter fashions in four different months. From a population of women, 18-21 years of age, a random sample of 100 women was selected in January. Another random sample of 100 women was selected in March. Another random sample of 100 women was selected in June. Another random sample of 100 women was selected in September.

A. The number of samples was 4.

B. The number of samples was 100.

C. The number of samples was 400.

D. The number of samples was 1.

Truck tire life is normally distributed with a mean of 60,000 miles and a standard deviation of 4,000 miles. You bought four tires. What is the probability that the average mileage of the four tires exceeds 66,000 miles?

A. 0.0013

B. 0.9987

C. 0.4987

D. 0.9544

A group of statistics students decided to conduct a survey at their university to find the average (mean) amount of time students spent studying per week. Assuming a population standard deviation of 6 hours, what is the required sample size if the error should be less than ½ hour with a 95% level of confidence?

A. 554

B. 130

C. 35

D. 393

A group of statistics students decided to conduct a survey at their university to find the average (mean) amount of time students spent studying per week. Assuming a population standard deviation of 3 hours, what is the required sample size if the error should be less than ½ hour with a 99% level of confidence?

A. 196

B. 240

C. 15

D. 16

Assuming a population standard deviation of 3 hours, what is the required sample size if the error should be less than ½ hour with a 99% level of confidence?

A. 196

B. 240

C. 15

D. 16

A survey of 50 retail stores revealed that the average price of a microwave was $375 with a standard error of $20. Assuming the population is normally distributed, what is the 95% confidence interval to estimate the true cost of the microwave?

A. $323.40 to $426.60

B. $328.40 to $421.60

C. $350.80 to $395.80

D. $369.31 to $380.69

To conduct a test of hypothesis with a small sample, we need to be able to make an assumption that:

A. a larger computed value of t will be needed to reject the null hypothesis.

B. the region of acceptance will be wider than for large samples.

C. the confidence interval will be wider than for large samples.

D. the population is normally distributed.

If the critical z-value for a test statistic equals 2.45, what value of the test statistic would provide the least chance of making a Type I error?

A. 3.74

B. 10,000

C. 2.46

D. 4.56

A recent study focused on the number of times men and women send a Twitter message in a day. The information is summarized below.

Men Sample size-25 Sample mean-20 Population standard deviation-5

Women Sample size-30 Sample mean-30 Population standard deviation-10

At the .01 significance level, is there a difference in the mean number of times men and women in a day? What is the test statistic for this hypothesis?

A. z-statistic

B. t-statistic

C. p-statistic

D. df-statistic

A recent study focused on the number of times men and women send a Twitter message in a day. The information is summarized below.

Men Sample size-25 Sample mean-20 Population standard deviation-5

Women Sample size-30 Sample mean-30 Population standard deviation-10

At the .01 significance level, is there a difference in the mean number of times men and women send a Twitter message in a day? What is the p-value hypothesis test?

A. Reject the null hypothesis and conclude the means are different.

B. Reject the null hypothesis and conclude the means are the same.

C. Fail to reject the null hypothesis and conclude the means are the same.

D. Fail to reject the null hypothesis and conclude the means are different.

When testing the difference between two population means, the variances are pooled when

A. the population standard deviations are known and equal.

B. the population means are known.

C. the population standard deviations are assumed unequal and unknown.

D. the population standard deviations are assumed equal but unknown.

When is it appropriate to use the paired difference t-test?

A. Four samples are compared at once

B. Any two samples are compared

C. Two independent samples are compared

D. Two dependent samples are compared

20 randomly selected statistics students were given 15 multiple-choice questions and 15 open-ended questions - all on the same material. The professor was interested in determining which type of questions the students scored higher. This experiment is an example of

A. a one sample test of means.

B. a two sample test of means

C. a paired t-test

D. a test of proportions

What is the variable used to predict the value of another called?

A. Independent variable

B. Dependent variable

C. Correlation variable

D. Variable of determination

What does a coefficient of correlation of 0.70 infer?

A. Almost no correlation because 0.70 is close to 1.0

B. 70% of the variation in one variable is explained by the other

C. Coefficient of determination is 0.49

D. Coefficient of nondetermination is 0.30

A hypothesis test is conducted at the .05 level of significance to test whether or not the population correlation is zero. If the sample consists of 25 observations and the correlation coefficient is 0.60, what is the computed value of the test statistic?

A. 1.96

B. 2.07

C. 2.94

D. 3.60