Statistics and Probability Answers

30% rate of catching the burglar; 60% rate of conviction; what the probability of both

In a certain city, the probability of catching a burglar is 30% with a 60% conviction rate. What's the probability of catching and convicting the burglar.

3. Rumor has it, going to class and reading the textbook will improve your chances of doing well (i.e., better than average) in stat’s class. You notice that there are four students in the class that always go to class and review the textbook everyday. To determine if the rumors are true, you ask those four students their marks on the quiz and find that their scores are:

60 60 61 67

Based on these scores and the knowledge that the exam scores are normally distributed (μ=50, σ=10), what can you conclude about the effect of going to every class and reviewing the textbook everyday on marks on the quiz? Do you reject or fail to reject the null hypothesis? What is the effect size? Assuming α=0.05, state your hypotheses, the critical test statistic, your conclusion, and show all your work.

The quality control officer of a certain firm specializing in manufacturing female T-shirts of varing shoulder sizes wishes to find out the mean shoulder size of all the T-shirts produced. She takes a random of 150 T-shirts which gave a mean shoulder size of 16 inches and a standard deviation of 2 inches. Construct a 98% confidence interval for the mean shoullder size of all the T-shirts produced by the company.

ANOVA (Analysis of Variances)


The following are data cholesterol levels of 60 employees.
X
205 327 189 205 148 139 178 157 188 301
195 185 164 182 201 248 298 264 177 169
174 169 155 188 194 192 177 189 188 176
158 305 248 189 209 159 202 177 278 268
166 285 249 203 199 170 165 180 201 209
301 188 165 173 183 206 202 283 207 156

a. Find the mean, median, mode, and standard deviation for X from the data given below.
b. In the frequency distribution for the data.

On an achievement test the mean and standard deviation for grade 7 males were 58 and 8.1 respectively. On the same test the mean and standard deviation for grade 7 female students were 62.0 and 9.0 respectively.
a. What percentage of 7th grade male scores fall above the mean of 7th grade female students?

b. What percentage of 7th grade female scores fall above the mean of 7th grade male students?

The paired t-test

Based upon the results of a manual dexterity test, two matched groups of female college students were formed. One group of students was asked to drive an automobile simulator after having consumed three bottles of beer in one hour. The second group of students drove the same simulator after consuming three bottles of nonalcoholic beer in the same time period. The number of errors per minute was recorded in the simulator as shown below. Is there a significant decrease in the errors per minute recording of the nonalcoholic group? Use an alpha level of 0.01.

Alcohol 6 4 9 3 15 5 9 7 6 8
Non-alcohol 5 5 6 0 8 2 4 2 8 4

Independent-samples t-test

A team of investigators has good reason to believe that a small dosage of a certain drug changes the speed with which people can make decisions. They decide to try to confirm this by carrying out an experiment in which the decision times of 14 people who have taken the drug are compared with those of a control group of 14 other people who have performed the task under a placebo condition. The experimenters expect that the average decision time of the experimental group will differ from that of the placebo group. The results are shown the following Table
Drug group
Case: 1 2 3 4 5 6 7 8 9 10 11 12 13 14
Time:390 494 386 323 660 406 345 425 421 407 386 550 470 393

Placibo Group
Case: 15 16 17 18 19 20 21 22 23 24 25 26 27 28
Time: 446 749 599 460 390 477 556 440 471 501 492 392 578 398

Independent Samples t-test

Is there any evidence that leadership style (as measured by the amount of controlling behavior) differs between principals in urban and rural areas in Oromia? Data are provided in a Table below.
Urban
Mean = 78.6 Standard deviation = 16.70 N= 9
Rural
Mean = 69.10 Standard deviation = 19.31 N= 10

you roll a fair die 20 times and end up with getting 3 ones 4 twos 5 threes 0 fours 2 fives and 6 sixes what is the theoretical P(1,4)