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Fittoniya [83]
3 years ago
5

The average systolic blood pressure was found to be 140 mm for people who have high responsibility jobs, specifically investment

banking jobs. Heart attack is the leading cause of death in the US, and the American Medical Association (AMA) deems average systolic blood pressure of 140 mm as very high. The fitness instructors and AMA doctors recommend practicing Yoga. They believe that practicing yoga reduces blood pressure and hence is beneficial to people. To test this claim, a sample of 51 investment bankers who had previously been diagnosed with high blood pressure was chosen. Participants were trained and completed yoga exercises for six months. At the end of the six months, the average blood pressure for the sample was 139 mm with a standard deviation of 5 mm.
What would be the proper set of hypotheses?

Group of answer choices

A. H0: μ = 139, H1: μ ≠ 139
B. H0: μ = 140, H1: μ < 140
C. H0: μ = 140, H1: μ ≠ 140
D. H0: μ = 139, H1: μ < 139
Mathematics
1 answer:
9966 [12]3 years ago
3 0

Answer:

Option B)

H_{0}: \mu = 140\text{ mm}\\H_A: \mu < 140\text{ mm}

Step-by-step explanation:

We are given the following in the question:

Hypothesis:

The doctors and u=instructor claims that practicing yoga reduces blood pressure and hence is beneficial to people.

Population mean, μ =  140 mm

Sample mean, \bar{x} =  139 mm

Sample size, n = 51

Sample standard deviation, s = 5 mm

Thus, we can design the null hypothesis and alternate hypothesis as

H_{0}: \mu = 140\text{ mm}\\H_A: \mu < 140\text{ mm}

The null hypothesis states that the population have a blood pressure of 140 mm. The alternate hypothesis states that yoga reduces the blood pressure and the sample has a blood pressure less than 140 mm.

Thus, the correct answer is

Option B)

H_{0}: \mu = 140\text{ mm}\\H_A: \mu < 140\text{ mm}

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Could the inverse of a non-function be a function? Explain or give an example.
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Answer:

The inverse of a non-function mapping is not necessarily a function.

For example, the inverse of the non-function mapping \lbrace (0,\, 0),\, (0,\, 1),\, (1,\, 0),\, (1,\, 1) \rbrace\! is the same as itself (and thus isn't a function, either.)

Step-by-step explanation:

A mapping is a set of pairs of the form (a,\, b). The first entry of each pair is the value of the input. The second entry of the pair would be the value of the output.  

A mapping is a function if and only if for each possible input value x, at most one of the distinct pairs includes x\! as the value of first entry.

For example, the mapping \lbrace (0,\, 0),\, (1,\, 0) \rbrace is a function. However, the mapping \lbrace (0,\, 0),\, (1,\, 0),\, (1,\, 1) \rbrace isn't a function since more than one of the distinct pairs in this mapping include 1 as the value of the first entry.

The inverse of a mapping is obtained by interchanging the two entries of each of the pairs. For example, the inverse of the mapping \lbrace (a_{1},\, b_{1}),\, (a_{2},\, b_{2})\rbrace is the mapping \lbrace (b_{1},\, a_{1}),\, (b_{2},\, a_{2})\rbrace.

Consider mapping \lbrace (0,\, 0),\, (0,\, 1),\, (1,\, 0),\, (1,\, 1) \rbrace\!. This mapping isn't a function since the input value 0 is the first entry of more than one of the pairs.

Invert \lbrace (0,\, 0),\, (0,\, 1),\, (1,\, 0),\, (1,\, 1) \rbrace\! as follows:

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  • (1,\, 0) becomes (0,\, 1).
  • (1,\, 1) becomes (1,\, 1).

In other words, the inverse of the mapping \lbrace (0,\, 0),\, (0,\, 1),\, (1,\, 0),\, (1,\, 1) \rbrace\! would be \lbrace (0,\, 0),\, (1,\, 0),\, (0,\, 1),\, (1,\, 1) \rbrace\!, which is the same as the original mapping. (Mappings are sets. There is no order between entries within a mapping.)

Thus, \lbrace (0,\, 0),\, (0,\, 1),\, (1,\, 0),\, (1,\, 1) \rbrace\! is an example of a non-function mapping that is still not a function.

More generally, the inverse of non-trivial ellipses (a class of continuous non-function \mathbb{R} \to \mathbb{R} mappings, including circles) are also non-function mappings.

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<h3>When do we perform one sample z-test?</h3>

One sample z-test is performed if the sample size is large enough (n  > 30) and we want to know if the sample comes from the specific population.

For this case, we're specified that:

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The z-test statistic we get is:

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Thus, we accept the alternate hypothesis that customer spends more in his store than the national average.

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