Consider the following information to validate the hypothesis that the mean of the population
is at most 30 at 5% level of significance.
Sample size = 45, mean of the sample = 38, variance = 4
What will be conclusion if the level of significance is taken as 1%? Mention the observations, if
any.
the botanist decided to count the number of daisies x in each of the 80 randomly selected squares with the field. find the mean and variance
A box contains 8 balls of the same size but different colours. 4 are red, 3 are blue and 1 is white. If a ball is selected at random,
6.1 What is the probability that a red ball will be selected ? (1)
6.2 What is the probability that a blue or a white ball will be selected? (3)
6.3 What is the probability that a white ball will be selected?
The QC points for the following days are as follows.
Day 6: 68
Day 7: 67
Day 8: 66
This is indicative of which type of error (systematic or random)? What could lead to this type of error? Give at least one example.
1. Do any of these data points violate any Westgard rules? If yes, indicate what rule and whether that rule calls for a rejection of the QC run. (5 points)
a. Day 1: 72.2
b. Day 2: 71.4
c. Day 3: 71.6
d. Day 4: 72.8
e. Day 5: 70.8
What is the area to he right of 1.5 under the t-distribution with 14 degrees of freedom?
What is the area to the right of 2.75 under the t-distribution with 28 degrees of freedom?
What is the area to the left of 2.8 under the t-distribution with 5 degrees of freedom?
If the degree of freedom is 20,what is the 96th percentile of the t-distribution?
In a t-distribution with 13 degrees of freedom, what is the 38th percentile?
Take the following set of numbers.
72
72
73
72
73
73
72
72
72
71
1. The lab that generated this data uses a standard acceptable Quality control range of -2SD-+2SD. Using the data above, determine if each of the following data points is out of range: (5 points)
a. Day 1: 72.2
b. Day 2: 71.4
c. Day 3: 71.6
d. Day 4: 72.8
e. Day 5: 70.8
An economist conducted a study to identify the percentage of family income allocated to the purchase of groceries. She surveyed a random sample of 50 families and compiled the following numeric frequency distribution:
Percent of income
Number of families
10 – under 20% 6
20 – under 30%
14
30 – under 40%
16
40 – under 50%
10
50 – under 60%
4
2.2.1 Compute and interpret the (approximate) mean percentage of family income allocated to grocery purchase. (Hint: Use the weighted average formula with the midpoint of each interval as xi.
5.1 Vehicles pass through a junction on a busy road at an average rate of 60 per hour.
5.1.1 Find the probability that none passes in a given 30-minute interval. (4)
5.1.2 What is the expected number passing in two minutes? (2)
5.1.3 Find the probability that this expected number (computed in 5.1.2) actually pass through in
a given five-minute period. (4)
5.2 Experience has shown that 80/200 of all CDs produced by a certain machine are defective. If a
quality control technician randomly tests twenty CDs, compute each of the following
probabilities:
5.2.1 P (exactly one is defective).
5.2.2 P (at least one CD is defective).
5.2.3 P (no more than two are defective).
5.2.4 Find the mean, variance and standard deviation of the distribution.
(3) (4) (5)
In a public senior high school, a survey conducted last year by the barangay health workers showed that 10% of the students drink alcohol. This year, a new survey was conducted randomly on 320 students from the same school and it was found out that 28 of them drink alcohol. Determine if the claim that there is a decrease on the proportion of senior high school students who drink alcohol is true. Use α = 0.05.