9. Find the 90% confidence for the difference of the means in Exercise 1 of this section.
Addition Rule of Probability
It simply refers to the likelihood of an event taking place whenever the occurrence of an event is uncertain. The probability of a single event can be calculated by dividing the number of successful trials of that event by the total number of trials.
Expected Value
When a large number of trials are performed for any random variable ‘X’, the predicted result is most likely the mean of all the outcomes for the random variable and it is known as expected value also known as expectation. The expected value, also known as the expectation, is denoted by: E(X).
Probability Distributions
Understanding probability is necessary to know the probability distributions. In statistics, probability is how the uncertainty of an event is measured. This event can be anything. The most common examples include tossing a coin, rolling a die, or choosing a card. Each of these events has multiple possibilities. Every such possibility is measured with the help of probability. To be more precise, the probability is used for calculating the occurrence of events that may or may not happen. Probability does not give sure results. Unless the probability of any event is 1, the different outcomes may or may not happen in real life, regardless of how less or how more their probability is.
Basic Probability
The simple definition of probability it is a chance of the occurrence of an event. It is defined in numerical form and the probability value is between 0 to 1. The probability value 0 indicates that there is no chance of that event occurring and the probability value 1 indicates that the event will occur. Sum of the probability value must be 1. The probability value is never a negative number. If it happens, then recheck the calculation.
![Exercises 9-3
the
For these exercises, perform each of these steps. Assume
that all variables are normally or approximately normally
distributed.
Use
Ch
a. State the hypotheses and identify the claim.
b. Find the critical value(s) or use the P-value method.
c. Compute the test value.
d. Make the decision.
e. Summarize the results.
N
6.
Use the traditional method of hypothesis testing unless
the P-value method is specified by your instructor. Assume
the variances are unequal.
1. Waterfall Heights Is there a significant difference
at a = 0.10 in the mean heights in feet of waterfalls in
Europe and the ones in Asia? The data are shown.
In Europe
Asia
487
1246
1385
614
722
964
470
1312
984
1137
320
830
900
345
820
350
722
1904
Source: World Almanac and Book of Facts.
2. Tax-Exempt Properties A tax collector wishes to see
if the mean values of the tax-exempt properties are dif-
ferent for two cities. The values of the tax-exempt prop-
erties for the two random samples are shown. The data
are given in millions of dollars. At a = 0.05, is there
enough evidence to support the tax collector's claim
that the means are different?](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F29cec45d-863c-4895-b2e1-cb73ae72e43f%2F102fd66b-6922-47f9-a351-f716202040c5%2F3d72wrd_processed.jpeg&w=3840&q=75)
![10.4
12.6
10.6
10.2
8.8
9.5
11.1
14.7
9.6
9.5
11.2
10.3
10.8
12.9
10.1
9.3
11.7
13.3
9.4
9.5
5
12.8
14.5
9.8
10.3
11.0
9
8. Teacher Salaries A researcher claims that the mean
of the salaries of elementary school teachers is greater
than the mean of the salaries of secondary school teach-
ers in a large school district. The mean of the salaries
of a random sample of 26 elementary school teachers is
$48,256, and the sample standard deviation is $3,912.40.
The mean of the salaries of a random sample of 24 sec-
ondary school teachers is $45,633. The sample standard
deviation is $5533. At a = 0.05, can it be concluded that
the mean of the salaries of the elementary school teachers
is greater than the mean of the salaries of the secondary
school teachers? Use the P-value method.
9. Find the 90% confidence for the difference of the means
in Exercise 1 of this section.
10. Find the 95% confidence interval for the difference of the
means in Exercise 6 of this section.
11. Hours Spent Watching Television According to
Nielsen Media Research, children (ages 2-11) spend
an average of 21 hours 30 minutes watching television
per week while teens (ages 12-17) spend an average
of 20 hours 40 minutes. Based on the sample statis-
tics shown, is there sufficient evidence to conclude a
9-19](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F29cec45d-863c-4895-b2e1-cb73ae72e43f%2F102fd66b-6922-47f9-a351-f716202040c5%2Fvyzb68j_processed.jpeg&w=3840&q=75)
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