Statistics and Probability Answers

It is a point such that 90% of the distribution lies below it and 10% lies above

1. The average score in the entrance examination in Mathematics at Sto.

Rosario National High School is 80 with a standard deviation of 10.A

random of 40 students was taken from this year's examinees and

was found to have a mean score of 84.

Is there a significant difference between the known mean and the

sample mean? Test at a= 0.05

Solution :

Step 1. H0: = 80 : There is no significant difference

hypothesized and the sample mean.

H1: "\\neq" 80 :

Step 2. Level of significance. a = 0.05.

Step 3. two tailed test, find the critical value. Zt =

4. Compute the test-statistic value:

5. Step :

6. Conclusion:

. Consider Interest centers on the life of an electronic component. Suppose it is known that the probability that the component survives for more than 6000 hours is 0.42. Suppose also that the probability that the component survives no longer than 4000 hours is 0.04. Determine the Probability that;

(a) The life of the component is less than or equal to 6000 hours?

(b)The life is greater than 4000 hours? 

According to a genetics theory,a certain cross of guinea pigs will result in red,black, and white offspring in the ratio 8:4:4.Find the probability that among 8 offspring,5 will be red,2 black, and 1 white.

Off-road motorbike racing can be dangerous, especially when it rains. It has been found that it rains during

18% of races. When it does not rain, there is a 5% chance that Dwayne (a rider) will get hurt. However, when it

rains, the chance that he gets hurt increases to 35%. Dwayne has just finished a race and is hurt. What is the

probability that it rained during the race?

QUESTION: A study believes that 70% of adults in the Philippines own a cellphone.

A cellphone manufacturer believes that the actual number is much

less than 70%. 100 Filipino adults were surveyed, of which 74 have

cellphones. Using a 5% level of significance, is the cellphone

manufacturer’s claim valid or not?

CLAIM:

EVIDENCE:

REASONING:

Directions: Draw a conclusion for the given situation using the five-step hypothesis testing

procedure for population proportion in both methods (critical value method and

the p-value method)

1. A nationwide poll claims that the country’s president has a less than 64% approval rating.

In a random sample of 120 people, 69 of them gave the president a positive approval

rating. Test the claim at 0.05 level of significance.

An association of City Mayors conducted a study to determine the average number of times a family went to buy necessities in a week. They found that the mean is 4 times in a week. A random sample of 20 families were asked and found a mean of 5 times in a week and a standard deviation of 2. Use 5% significance level to test that the population mean is not equal to 5. Assume that the population is normally distributed.

A garment factory distributes two brands of jeans. If it is found that 75 out of 250 customers prefer brand A and that 30 out of 150 prefer brand B, can we conclude at 0.05 level of significance that brand A outsells brand B?

A study claims that on average, male high school students spend at least 3.39 hours a day playing video games with a standard deviation of 2.05 hours. A random sample of 30 teenagers were surveyed and the results showed that these teenagers spend 4.12 hours a day playing video games.

What is the null hypothesis for the given problem?