PLEASE SOLVE A) B) C) Use alpha 0.05 Problem #2. (16 pts) Data on the amount spe

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PLEASE SOLVE A) B) C) Use alpha 0.05
Problem #2. (16 pts) Data on the amount spent at "Jonny's dry cleaner, (in dollars) by a sample om costumes was collected: 17.42 16.29 17.55 16.02 18.98 18.83 19.00 (5 pts) The researcher is interested in testing whether the mediar amount spent is greater than $16.50. Knowing that the amount spent at the dry cleaner is distributed as a binomial X-Bin (7.5), compute the p-value for the test (and write your answer in the box): p- b. (8 pts) More data were collected from the same dry cleaner and added to the previous data. The available data is now: 7.42 16.29 18.00 16.02 18.98 18.83 19.00 18.00 16.50 16.50 Now the researcher wants to test whether the median amount spent is less than $18.00 The statistics for the test is S and the amount spent for lunch is a random variable with binomial

Explanation / Answer

a. Hypothesis : Ho:me = 16.5 ag. H1: me > 16.5

Here, we will use the one sample sign test since the underlying distribution is already stated as Binomial Distribution.

So the number of observations greater than the median value under Ho(=16.5) i.e., the number of positive signs = 5

Similarly the number of negative signs = 2

Since out of 7 observations, 5 are positive and the rest 2 are negative, we can say that the distribution of the positive signs follow a binomial distribution i.e., r~bin(7, 0.5)

So our hypothesis becomes :

Ho: r = 5 ag. H1: r > 5

So r here is our test statistic representing the no. of positive signs in the given sample.

Hence the p-value = P[ r>5]

= (7c6)*(1/2)^6 +(7c7)*(1/2)^6

= 1/8

b. The hypothesis to be tested :

Ho: m = 18 ag. H1: m < 18

We'll again use the one sample sign test. This time the number of positive signs under the median value is = 4

Similarly the number of negative signs = 6

If r be the number of positive signs out of 10 observations then r~bin(10, 1/2)

Therefore the test statistic is S = r

And the amount spent has the distribution bin( 10, 1/2)

If the computed p-value is p =0.172, we'd conclude that there IS statistical evidence to support the research hypothesis since : under Ho: p=0.5 and our testing rule was - "reject H0 if P observed < P given

c. The Kruskal-Wallis test is the best test for testing whether there is significant difference between 2 medians.

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