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Digiron [165]
3 years ago
6

In a recent​ study, volunteers who had 8 hours of sleep were three times more likely to answer questions correctly on a math tes

t than were​ sleep-deprived participants. 
Mathematics
1 answer:
Shalnov [3]3 years ago
3 0

Answer:

Step-by-step explanation:

Sleep Deprivation

In a recent study, volunteers who had 8 hours of sleep were three times more likely to answer correctly on a math test than were sleep-deprived participants.

(a) Identify the sample used in the study.

(b) What is the sample's population?

(c) Which part of the study represents the descriptive branch of statitics?

(d) Make an inference based on the results of the study?

Solution

A. The samples used is the hours of sleep and math test scores of the volunteers

B. The samples population is hours of sleep and math test scores of people in general

C. The part of the study that represent the descriptive branch of statistics is "three times more likely"

D.Inference: To perform well in a math test, a person should get at least 8 hours of sleep the night before.

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The amount that households pay service providers for access to the Internet varies quite a bit, but the mean monthly fee is $50
Natali5045456 [20]

Answer:

(a) See Explanation

(b) \bar x =50 and \sigma_x = 0.8944

(c) The shape is normal

(d) P(\bar x > 55) = 0

Step-by-step explanation:

Given

\mu = \$50 -- mean

\sigma = \$20 --- standard deviation

n=500 --- sample size

Solving (a): The reason we can't determine the probability that an amount to access internet by a household will exceed $55.

The question says that a lot of households pay low rates, but the percentage of the households in this category is not given. This means that it is impossible to determine the shape of the distribution.

Hence, the probability cannot be calculated.

Solving (b): Sample mean and Sample standard deviation

The sample mean estimates the population mean

So:

\bar x =\mu

\bar x =50

The sample standard deviation is calculated as thus:

\sigma_x = \frac{\sigma}{\sqrt n}

\sigma_x = \frac{20}{\sqrt{500}}

\sigma_x = \frac{20}{22.36}

\sigma_x = 0.8944

Solving (c): The shape of the distribution.

We have:

n = 500 --- The sample size

According to Central limit theorem, When the sample size is greater than 30, then the shape of the distribution is normal.

<em>Hence, the shape is normal</em>

Solving (d): P(\bar x \ge 55)

Calculate the test statistic (t)

t = \frac{\bar x - \mu}{\sigma}

t = \frac{55 - 50}{0.8945}

t = \frac{5}{0.8945}

t = 5.590

So:

P(\bar x > 55) = P(t > 5.590)

Referencing the z table, we have:

P(t > 5.590) = 0

Hence:

P(\bar x > 55) = 0

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