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Kitty [74]
2 years ago
10

400 students were randomly sampled from a large university, and 289 said they did not get enough sleep. Conduct a hypothesis tes

t to check whether this represents a statistically significant difference from 50%, and use a significance level of 0. 1
SAT
1 answer:
jarptica [38.1K]2 years ago
4 0

Answer:

The sample proportion represents a statistically significant difference from 50%

Explanation:

The sample proportion is the same as 50%

Alternate hypothesis: The sample proportion is not the same as 50%

z = (p' - p) ÷ sqrt[p(1 - p) ÷ n]

p' is sample proportion = 289/400 = 0.7225

p is population proportion = 50% = 0.5

n is number of students sampled = 400

z = (0.7225 - 0.5) ÷ sqrt[0.5(1 - 0.5) ÷ 400] = 0.2225 ÷ 0.025 = 8.9

The test is a two-tailed test. Using a 0.01 significance level, critical value is 2.576. The region of no rejection of the null hypothesis is -2.576 and 2.576.

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About ​% of the population of a large country is. If two people are randomly​ selected, what is the probability both are ​? what
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Using the binomial distribution, it is found that there is a:

  • 0.0036 = 0.36% probability that both are allergic to pollen.
  • 0.1164 = 11.64% probability that at least one is allergic to pollen.

<h3>What is the binomial distribution formula?</h3>

The formula is:

P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}

C_{n,x} = \frac{n!}{x!(n-x)!}

The parameters are:

  • x is the number of successes.
  • n is the number of trials.
  • p is the probability of a success on a single trial.

Researching the problem on the internet, it is found that:

  • 6% of the population is allergic to pollen, hence p = 0.06.
  • Two people are chosen at random, hence n = 2.

The probability that both are allergic is P(X = 2), hence:

P(X = 2) = 0.06^2 = 0.0036.

0.0036 = 0.36% probability that both are allergic to pollen.

The probability of at least one is:

P(X >= 1) = 1 - P(X = 0) = 1 - 0.94^2 = 1 - 0.8836 = 0.1164.

0.1164 = 11.64% probability that at least one is allergic to pollen.

More can be learned about the binomial distribution at brainly.com/question/24863377

4 0
2 years ago
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