Math Answers

I. Determine the given of the problems below and formulate the null and alternative hypothesis both in words and symbols. Write your answer in your notebook. Please follow the format in the examples.

3. A kinder teacher developed a coloring worksheet for her pupils. Using this worksheet the pupil’s performance has a mean score of 90 and a standard deviation of 10. Fifty kinder pupils from a certain barangay were asked to answer the said worksheet and found that their mean score was 95 with a standard deviation of 5. Test the hypothesis at 1% significance level.

H0: ________________________________________________________________

Ha: ________________________________________________________________

Check whether the sequence (an), where

an = 1/ (n+1) + 1/(n+2) +....+1/(2n) is convergent or not

I. Determine the given of the problems below and formulate the null and alternative hypothesis both in words and symbols. Write your answer in your notebook. Please follow the format in the examples.

1. A jeepney driver claims that his average monthly income is Php 3000.00 with a standard deviation of Php 300.00. A sample of 30 jeepney drivers were surveyed and found that their average monthly income is Php 3500.00 with a standard deviation of Php 350.00. Test the hypothesis at 1% level of significance.

H0: _____

Ha: _____

2. A mathematics teacher in senior high school developed a problem-solving test to randomly selected 40 grade 11 students. These students had an average score of 85 and a standard deviation of 5. If the population had a mean score of 90 and a standard deviation of 3, use 5% level of significance to test the hypothesis.

H0: _____

Ha: _____

Show that if 5/3< 2x< 11/3, then x∈{y∈R such that |y- 4/3| < 1/2}

in a given city 6% of all drivers get at least one parking ticket per year . use the position approximation to the binomial distribution to determine the probabilities that among 80 drivers (randomly choosen in the city). (1) 4 will get at least one parking ticket in any given year, (2)at least 3 will get one parking ticket in any given year, (3)anywhere from 3 to 6 inclusive ,will get at least one parking ticket in any given year​

2. One of the undersecretaries of the Department of Labor and Employment (DOLE) claims that the average salary of a civil engineer is Php 18,000. A sample of 19 civil engineer's salary has a mean of Php 17,350 and a standard deviation of Php 1,230. Is there enough evidence to reject the undersecretary's claim at a = 0.01?

Solution:

step 1: null and alternative hypothesis

H0:__________

H1:__________

step 2: Significance level a =__________

step 3: test statistic

step 4: decision rule

step 5: decision

 Which of the following is a parameter in the situation “A machine which has been regulated dispenses an average of 330 ml fruit concentrate per bottle. A random sample of 49 bottles filled by the machine has a mean content of 320 ml and a standard deviation of 50 ml.”?

An aeroplane heads due north at 500km/h. It experiences a 80km/h cross wind flowing in the direction N60 degrees E

find the true velocity of the aeroplane

determine the died of the aeroplane.