# Economic statistics Essay Example

Statistics 4

Subject: Economic Statistics

Question 1

1. Critical value approach

1. Null and alternate hypothesis

1. The level of significance is 5%

2. Test statistic is student’s t-test

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

1. The level of significance is 5%

2. Test statistic is student’s t-test

1. 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

Question 3

Breaks down 6 times per 30-day period

Probability of suffering heart attack: 45%

Sample 100 middle-age balding men

Question 4

Each has a different color marked differently

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

 Samples of size 2

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

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

Claim: 50% satisfied

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

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

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

Hence

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

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

X is binomial random variable

Number of trials (n)=100