Statistics and Probability Answers

I. State the null and alternative hypothesis for each statement.

1. A light bulb manufacturer claims that the mean life of a certain type of light bulb is more than 750 hours.

  H_{0: _____}

  H_{a: _____}

2. A study claims that the mean survival time for certain cancer patients treated immediately with chemotherapy and radiation is 24 months.

  H_{0: _____}

  H_{a: _____}

3. A medical trial is conducted to test whether or not a new medicine reduces uric acid by 50%.

  H_{0: _____}

  H_{a: _____}

4. We want to test whether the general average of students in Math is different from 80%.

  H_{0: _____}

  H_{a: _____}

5. We want to test whether the mean height of Grade 8 students is 58 inches.

  H_{0: _____}

  H_{a: _____}

a seller claim that her lip tint has a mean organic content of 90%. A rival seller asked 60 users of that lip tint and found that it has a mean organic content of 85% with a standard deviation of 5%. test the claim at 1% level of significance and assume tha the population is approximately normally distributed

A chemical company alleged that the average weight of the bag of chemical is 30kgs. with a standard deviation of 1.1 kgs. A sample of 26 bags was taken and revealed a mean weight of 28.9 kgs. Shall we accept the allegation of the chemical company? Use .01 level of significance

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 8 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 = 7. (Set the significance level➔ = .05) 

Find P( -1.2 < Z < -0.2 )

Given: Margin of error (d)= 2.19, Confidence interval (CI) of population mean = 90%, and population standard deviation (σ)= 5 solve for the appropriate sample size.

In a study made on time and motion, it was found out that a certain manual work can be finished at an average time of 40 minutes with a standard deviation of 18 minutes. A group of 16 workers is given a special training and then found to average only 35 minutes. Can we conclude that the special training can speed up the work using a 0.05 level?