### Question Description

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

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## Final Answer

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Attached.

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...

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