Statistics and Probability Answers

Fifteen trainees in a technical program are randomly assigned to three different types of

instructional approaches, all of which are concerned with developing a specified level of skill

in computer-assisted design. The achievement test scores at the conclusion of the

instructional unit are reported in Table along with the mean performance score associated

with each instructional approach. Use the analysis of variance procedure to test the null

hypothesis that the three-sample means were obtained from the same population, using the

5 percent level of significance for the test.

Previous record has indicated that the breaking strength of cables used in textile industries is normally distributed with a known variance of 25KN/m2 . A random sample of ten cables is tested resulting in the following yields: 250 225 190 188 210 210 198 230 233 231 Construct a 98% confidence interval on the true average breaking strength.

1.     The manager of a supermarket collected the data of 25 customers on a certain date. Out of them 5 purchased Biscuits, 10 purchased Milk, 8 purchased Fruits, 6 purchased both Milk and Fruits.

Let B represents the randomly selected customer purchased Biscuits, M represents the randomly selected customer purchased Milk and F represents the randomly selected customer purchased Fruits.

Represent the given information in a Venn diagram. Use that Venn diagram to answer the following questions.

a)        Find the probability that a randomly selected customer either purchased Biscuits or Milk.

b)        Show that the events “The randomly selected customer purchased Milk” and “The randomly selected customer purchased Fruits” are independent.

 A company produced ethyl alcohol and claimed to have a mean alcohol content of

70%. A random sample of 80 of ethyl alcohol was take as sample to verify this claim. It

was found out that the mean alcohol content is 65% with a standard deviation of 2%. Test

the claim at 5% level of significance and assume that the population is normally

distributed​

what is the t-value for a 90% confidence interval with n = 10

The number of accidents in a highway as recorded every month over a 9 - month periods are 15,18,9,11,14,10,8,13,19. Test at 5% frequencies are in agreement with the belief that the number of accidents was the same during the 9 - months. it is given that the table values of x² at 5% level for 8 d.o.f and 9 d.o.f . are 15.5 and 16.9 respectively.

According to last year’s report, a filipino household spends an average of P400/day for food. Suppose you took a sample of 25 households. You determined how much each household spent for the food daily and the results revealed a mean of P380 and a standard deviation of P21.50. with 99% confidence what would be your conclusion

The mean score of the first periodic exam in Statistics is 89 and the standard deviation is 12. One student believed that the mean was less than this, she then randomly selected 34 students and computed their mean score. She obtained that the mean score of 85 at 99% confidence. Test the student belief. Use both method to evaluate

The owner of a mobile phone store in Greenhills shopping center was not happy when he learned that the average number of cellphones sold daily was 8 items only. He hired a new seller and was told to tally the daily sales for 20 days. The new sale records are 9, 9, 9, 8, 9, 9, 11, 12, 12, 16, 10, 12, 8, 11, 17, 18, 15, 14, 17, and 14. by using the default significant level do the collected data enough to indicate that their sale got increased?

Based on a​ poll, 69​% of Internet users are more careful about personal information when using a public​ Wi-Fi hotspot. What is the probability that among four randomly selected Internet​ users, at least one is more careful about personal information when using a public​ Wi-Fi hotspot? How is the result affected by the additional information that the survey subjects volunteered to​ respond?