 Mathematics
Inference In Practice A Population Mean And Confidence Intervals

### Question Description

All work and explanations required

Inference in practice; Inference about a Population Mean; confidence intervals; The one-sample t confidence interval

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True/False
1. T
If you were doing a two-tailed test of significance, you would need to divide the α by two, in order to
determine the critical region.
2. T
In order to determine the y-intercept in a regression problem, both the dependent variable and the
independent variable must be quantitative.
3. T
In a random sample of 48 observations from a normal distribution, there will be approximately 12
observations less than the 25th percentile.
4. F
In a one-tailed test where n=21, the value of the Z-test statistic equals -1.812. If α were set at 0.01,
this test would be considered significant
5. F

If a person had a z-score of 0.50, then their actual raw score has to be above the median.

6. T
If a statistical test is significant at the 10% (alpha = 0.10) level, then it may or may not be significant
at the 5% (alpha = 0.05) level.
7. T
A correlation coefficient estimated to be close to +1.0 , would be considered to be a very strong
linear relationship.
8. F
If a 99% CI for the population mean age is calculated to be [36yrs, 46yrs]; then this implies that
approximately 1% of the population will be older than 46 years old.
9. T
A test of H0 : μ = 50 against H 1 : μ < 50 has test statistic t = -2.35, for n=21. This test would
be considered statistically significant at α = 0.01.
10. F
In estimating the true population mean, if you decrease the level of confidence (say 99% to 90%),
then the widthe of the CI would also decrease.
FILL IN THE BLANK (Q11- Q20) WITH A NUMBER, A WORD OR A SHORT ANSWER
11.

Using the Z-table, find the value of Z such that
P (Z < 1.645) = 0.95

--------------------------------------------------------------------------------------------------------------------------------12.
Complete the following sentence. The P-value of a test is the probability of the occurrence of a specific
event.
13.
In performing a two-tailed test for n= 18, the t-test statistic equals 2.10. If alpha = .05, what are the two
critical values from the t-table that would define the acceptance and rejection regions?
-2.567, +2.567
-------------------------------------------------------------------------------------------------------------------------------------14.
In a distribution, the mean = 158, the mode = 155 and the median = 152 and the standard deviation =12.
Which way is the distribution skewed? The distribution has a longer right tail. (Positively skewed/right skewed)
.
Why? The mean is greater than the
mode and median, thus only has a few relatively high values.

15.
Suppose age was normally distributed in a population with the mean = 62 and variance = 25. A person
whose age is 66 would have a z-score of 0.8
.
𝑍 = (𝑋 − µ) / 𝛿 = (66-62) / √25 = 0.8

.

16.

A random sample of part-time workers and the length of time (days) that they worked were recorded.
The following stem plot has a stem width of 5.
(a) ) Calculate the sample standard deviation
(b) are there any outliers? If so, what are they?
5|
5|
6|
6|
7|
7|
8|
8|
9|
9|

0
5
2
5
4
8
2
5
2
8

9
4
9
2
5
0
9

4
9
3
54
0

Std deviation = 2.996
Outliers: 0, 5 and 2
17. In recent years there has been a lot of discussion in the medical literature regarding the role of diet in the
development of heart disease. Suppose a sample of 18 individuals who eat primarily a vegetarian diet is randomly
taken. Their mean cholesterol is found to be 180 mg/dl. Suppose in the general population, the mean cholesterol is
205 mg/dl with a SD of 20mg/dl. Based on the sample data can you want to conclude that the mean cholesterol for
vegetarians is less than that of the ge... TutorAR (16702)
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