Economic statistics Essay Example

Statistics 4

Subject: Economic Statistics

Question 1

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  1. Critical value approach

  1. Null and alternate hypothesis

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  1. The level of significance is 5%

  2. Test statistic is student’s t-test

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  1. One tailed test

  2. At 5% level of significance, the critical value is 1.833

  3. The test statistic of 2.1082 lies beyond critical value of 1.833 hence null hypotheses is rejected and alternate accepted.

  1. P-value approach

  1. Null and alternate hypothesis

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  1. The level of significance is 5%

  2. Test statistic is student’s t-test

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    P-value is

  2. Reject null hypothesis because P-value of 0.0321 is less than significance level of 0.05.

It is apparent that both the critical value approach and the P-value approach give the same conclusion.

  1. The assumption that the number of cases is normally distribute dis important because it allows a comparison with the standard bell curve given by a particular mean and standard deviation.

Question 2

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Question 3

Breaks down 6 times per 30-day period

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Probability of suffering heart attack: 45%

Sample 100 middle-age balding men

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Question 4

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Each has a different color marked differently

  1. Possible samples of size n=2 from the population of 6 tokens.

Samples of size 2

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  1. Sampling distribution of sample means (X-bar)

sample mean

  1. The mean and the variance of the sampling distribution of X-bar

sample mean

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  1. . Hence, the mean of the sampling distribution is equal to the population mean. economic statistics 61
    Population mean is given by

Variance of the population is 2.9167 hence sampling variance is given by:

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Claim: 50% satisfied

  1. Probability that in a random sample of 600 customers less than 45% are satisfied

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  1. If in a random sample of 600 customers, 270 express satisfaction with the bookstore, this means that :

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Since the probability that less than 45% of customers will be satisfied is 0.7%, then the store is not efficient in delivering its services.

Question 5

Normally distributed random variable with a mean of 7.5 hours

Standard deviation of 2.1 hours

  1. The proportion of students studying for more than 10 hours per week

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Hence

  1. Proportion of A students that spend less than 3 hours studying

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  1. Amount of time below which only 5% of all A students spend studying:

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X is binomial random variable

Number of trials (n)=100

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