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A survey found that the average hotel room rate in Luzon is ₱2,300 and the average room rate in Mindanao is ₱2,150. Assume that the data were obtained from two samples of 75 hotels in Luzon and 80 hotels in Mindanao and the standard deviations were ₱250 and ₱215, respectively. At α=0.05, can it be concluded that there is a significant differences in the rates? (10 points)
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.
For a particular school year, the registrar of a university wanted to know the proportion of students who are enrolled in the Sciences. The enrollment data showed total enrollment of 6 534 students. Of this total, there were 4 286 enrolled in various Science courses. What do the numbers say about the course preferences of the students?
Given that the probability of error in transmitting a bit over a communication
channel is 8 × 10−4, compute the probability of error in transmitting a block
of 1024 bits. Note that this model assumes that bit errors occur at random,
but in practice errors tend to occur in bursts. Actual block error rate will be
considerably lower than that estimated here.
An electrical company claims that the average life of the bulbs it manufactures is 1 100 hours with a standard deviation of 200 hours. If a random sample of 110 bulbs is chosen, what is the probability that the sample mean will be between 1120 hours and 1 150 hours?
In a study to estimate the proportion of smokers among the residents in a certain city and its suburbs, it is found that 24 of 104 urban residents are smokers, while 34 of 108 suburban residents are smokers.
On an enquiry related to the frequent reporting of mouth cancer cases, it is estimated that around 60% of the patients chewed tobacco. Does this seem to be a valid estimate if, in a random sample of 120 people, 84 were found to be tobacco users?
1. "X_1,\\ldots,X_n \\sim iid \\sim N(0,1)." Define "\\bar{X}" (sample mean) and "S^2=\\sum_1^n X_i^2" .
a) Show that "\\bar{X}" and "S^2" are dependent.
b) Derive the conditional distribution of "\\bar{X}" , given "S^2".
c) Determine c(u) such that P["\\bar{X}" > c(u)|u] =alpha, where "\\text{u}=S^2".
The table below presented the ranks which were assigned by three judges to the works
of ten articles:
S.no. 1 2 3 4 5 6 7 8 9 10
Judge A 5 7 4 1 3 2 9 8 10 6
Judge B 4 8 3 2 7 1 10 6 9 5
Judge C 8 6 2 10 4 1 3 9 5 7
Compute the spearman’s rank order correlation coefficients for each pair of ranking and
decide:
a) Which two judges are most alike in their opinion about these artists?
b) Which two judges are different in their opinion about these artists?
The table below presented the ranks which were assigned by three judges to the works
of ten articles:
S.no. 1 2 3 4 5 6 7 8 9 10
Judge A 5 7 4 1 3 2 9 8 10 6
Judge B 4 8 3 2 7 1 10 6 9 5
Judge C 8 6 2 10 4 1 3 9 5 7
Compute the spearman’s rank order correlation coefficients for each pair of ranking and
decide:
a) Which two judges are most alike in their opinion about these artists?
b) Which two judges are different in their opinion about these artists?
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#340153 on Dec 2023