Question

Question B.3 [20 marks]

A manufacturing company in the electronic devices field is highly satisfied with the volume of sales of its smart TVs. Historical data suggest that the average profit is €71842 per month. Nevertheless, it seems that sales may have increased during recent years. Having considered the last 22 months to review, the average profit resulting from the sales of smart TVs is equal to €72083, while the population standard deviation is equal to €1682. You are required to perform a 0.05 significance hypothesis test to verify whether there is an increase in the smart TV sales profit.

Round the numerical answers to four decimal places.

PLEASE NOTE: In case the value of the test statistic (and associated probability) cannot be found exactly in the NCST, please use the nearest possible value and specify this occurrence in the solution of the exercise

1. State the null hypothesis.                                                         [2 marks]
2. State the alternative hypothesis.                                              [2 marks]
3. Do you reject the null hypothesis? Answer Yes or No and provide the decision rule.                                                             [3 marks]
4. State the type of hypothesis test.                                             [2 marks]
5. Compute the value of test statistic.                                           [2 marks]
6. What is the critical value to be used for the comparison?   [2 marks]If the critical value approach is performed:
7. Please provide a short interpretation of the outcome (one sentence max).                                                                               [1 mark]
8. Do you reject the null hypothesis? Answer Yes or No and provide the decision rule.                                                             [3 marks]
9. If the p-value approach is performed:
10. What is the p-value?                                                       [2 marks]

2. Please provide a short interpretation of the outcome (one sentence max).                                                                               [1 mark]

Answer 1

Short interpretation: We conclude that there is not enough evidence to suggest that there is an increase in the smart TV sales profit from $71842.