Statistics and Probability Answers

Ten patients with anorexia in the final stages of recovery were candidates for a trial of a new anti-anxiety drug. Patients received the drug over four weeks. Each patient was also given a placebo over four weeks. Anxiety scores were measured at the

end of each treatment period. The order of administration of the active drug and the placebo was randomized for each patient. There was a washout period of four weeks between the administration of the drug and placebo.

Was the new drug significantly more effective than the placebo in reducing patient anxiety?

1.     A nutrition store in the mall is selling “Memory Booster,” which is a concoction of herbs and minerals that is intended to improve memory performance, but there is no good reason to think it couldn't possibly do the opposite. To test the effectiveness of the herbal mix, a researcher obtains a sample of 26 participants and asks each person to take the suggested dosage each day for 4 weeks. At the end of the 4-week period, each individual takes a standardized memory test. In the general population, the standardized test is known to have a mean of μ = 50.

An electrical firm manufactures light bulbs that have a length of life that is approximately normally

distributed with a standard deviation of 40 hours. If a sample of 30 bulbs has an average life of 780

hours, find a 96% confidence interval for the population mean of all bulbs produced by this firm

Average undergraduate cost for tuition, other fees, and boarding for all institutions in the US last year is $19410. A random sample of costs this year for 40 institutions of higher learning indicated that the sample mean was $22098, and the sample standard deviation was $6050. At 0.01 level of significance, is there sufficient evidence to conclude that the cost has increased

Records of a health insurance company show that 30% of its policyholders over 50 submit a claim during the year. 15 policyholders over 50 are selected at random; what is the probability that at least 10 will submit a claim during the year? 

What is the probability that 4 will submit a claim during the year?

 How many do you expect to submit a claim?

What is the standard deviation?

A questionnaire asks shareholders of a company to state whether they consider the chairman’s salary to be too high, about right, or too low. Excluding shareholders who have no opinions, the probabilities of answers from random selected shareholders are as follows:

Too high 0.82

About right 0.12

Too low. 0.05

New employees at a manufacturing plant have to attend training program in order to become proficient in a certain piece of machinery. To test if the method of training affects the mean time taken to complete the assembly procedure, 18 new employees are randomly assigned to one of two different training methods: 9 undergo the training program A, and 9 undergo training program B. At the end of the training the time (in minutes) take by these employees to complete the assembly procedure is recorded. Assume that time taken follows a normal distribution. The data are summarised as follows:

 Program A Program B Difference (A – B)

Mean 36 31 5

Standard deviation 5.05 4.92 4.12

Which one of the following statements is false?

A. The pooled variance is 4.12

B. This is an independent samples t-test

C. This is a 2-sided test

D. The value of the test statistic is 2.1275

E. The test statistic follows a t-distribution with 16 degrees of freedom

est marks are assumed to follow a normal distribution. The test marks of 25 randomly selected students yielded a 99% confidence interval for the population mean of: (40.6; 71.9). When using this confidence interval to test the hypothesis that the mean is different from 60, which one of the following statements is false?

Group of answer choices

A. H₀: µ = 60  vs. H₁: µ > 60

B. This interval can only be used to test at the 1% level of significance

C. This interval can only be used to test a two-sided hypothesis

D. At the 1% level of significance there is insufficient evidence that the average test mark is not 60

E. Since 60 is included in the confidence interval, H₀ is not rejected

Which one of the following statements is true?

Group of answer choices

A. If α = 0.1 and we fail to reject the null hypothesis, the original assumption is accepted at the 10% level of significance

B. If a hypothesis is rejected at the 5% level of significance, it is also rejected at the 1% level of significance

C. In a 95% confidence interval, 95% of the values could be the value of the population parameter

D. Statements about sample statistics are tested through the process of hypothesis testing

E. The sample mean of the variable of interest is always in the middle of a confidence interval of the mean

State the importance of filter in time series analysis