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A population consists of five numbers 1, 2, 3, 4, 5 and 6. Suppose samples of size 2 are drawn from this population.


(a) Find the mean and variance of the population


(b) Describe the sampling distribution of the sample means.


(c) Find the mean and variance of the sampling distribution of the sample means.



Ask the use if they want a cup of tea. If they replay with “no” or “n” repeat the question. Once the loop stops display the message “Sorry,we have run out of tea”

Ask the user to input a number and then ask if they want to double the number. If they answer “y”multiply the number by 2 and display the answer. Keep repeating this loop, doubling their number each time, until they no longer reply “y”.

Average of the given numbers

Looping problem:-

Input two positive integers a and b from the user. Determine the remainder of a/b. Assume that the division and modulus operators are not available.


Looping problem:-

Input two positive integers a and b from the user. Determine the integer quotient of a/b. Assume that the division operator is not available.


Looping problem:-

Write an if-else statement that outputs the word "Warning" provided that either the value of the variable temperature is greater than or equal to 100, or the value of the variable pressure is greater than or equal to 200, or both. Otherwise, the if-else statement outputs the work "OK".


Three numbers denoted by the variables A, B and C are supplied as input data. Print these three numbers in ascending order.


Frequent checks on the spending patterns of tourists returning from countries in Asia were made and the average amount spent by all tourists was found to be R1010 per day. To determine whether there has been a change in the average amount spent, a sample of 70 travelers was selected and the mean was determined as R1090 per day with a standard deviation of R300. A researcher wants to test for evidence of a change in the expenditure amount changed, using 0.05 level of significance.

i. What is the appropriate distribution to use? Motivate your answer. [3]

ii. State your hypotheses. [2]

iii. Is there a claim? What is the claim and in which part of the hypothesis does the claim resides? [3]

iv. Use a distribution curve to determine the rejection and non-rejection region using critical values for the appropriate distribution. [5]

v. Calculate the test statistic of the distribution. [2]

vi. Compare your test statistic to the critical value. [2]

vii. State both your statistical and a management conclusion. [3]


Frequent checks on the spending patterns of tourists returning from countries in Asia were made and the average amount spent by all tourists was found to be R1010 per day. To determine whether there has been a change in the average amount spent, a sample of 70 travelers was selected and the mean was determined as R1090 per day with a standard deviation of R300. A researcher wants to test for evidence of a change in the expenditure amount changed, using 0.05 level of significance. What is the appropriate distribution to use? Motivate your answer


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