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1. A researcher estimates that the average height of the buildings of 30 or more stories in a large city is at least 700 feet. A random sample of 10 buildings is selected, and the heights in feet are shown. At = 0.025, is there enough evidence to reject the claim? 485 511 841 725 615 520 535 635 616 582
In student's t-distribution, if the sample size is 25, what is the degree of freedom?
II. 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.
2. A study was conducted to determine the marrying age of teachers. It was found out that the mean marrying ager of teachers is 30 years old. Fifteen teachers were surveyed randomly and found that their mean marrying age was 33 years old with a standard deviation of 5 years. Use 10% level of significance to test the hypothesis and assume that the population is normally distributed.
3. A study was conducted to determine the marrying age of teachers. It was found out that the mean marrying ager of teachers is 30 years old. Fifteen teachers were surveyed randomly and found that their mean marrying age was 33 years old with a standard deviation of 5 years. Use 10% level of significance to test the hypothesis and assume that the population is normally distributed.
II. 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 health specialist wants to determine the average number of hours a person exercise in a day during the quarantine period. She found out that the mean number of hours a person exercise in a day during the quarantine period is 80 minutes. A random sample of 29 persons were surveyed and found that their mean is 65 minutes and a standard deviation of 10 minutes. Test the hypothesis at 2% level of significance and assume that the population is normally distributed.
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
