6.3 Example: testing a hypothesis
Records shows that customers are willing to pay less than or equal to £2200 for an 8-day premium Iceland winter travel tour, with a standard deviation of £500. A marketing manager believes that customers are willing to pay more for such a tour. To test this belief, the marketing manager asks 45 customers how much they are willing to pay. Below are the responses that the marketing manager received from 45 customers (in the value of £). You now need to determine what the p-values are.
| £2300 | £2200 | £2500 | £2600 | £2100 |
| £2350 | £2450 | £2100 | £2000 | £2150 |
| £2300 | £2400 | £2500 | £2650 | £2750 |
| £2150 | £2800 | £2100 | £2000 | £2600 |
| £2400 | £2000 | £2300 | £2200 | £2100 |
| £2600 | £2500 | £2500 | £2400 | £2300 |
| £2500 | £2200 | £2250 | £2350 | £2550 |
| £2400 | £2400 | £2500 | £2450 | £2350 |
| £2250 | £2450 | £2650 | £2500 | £2400 |
Step 1: Based on the information statements above, you can formulate the hypotheses:
H0: Customers are willing to pay less than or equal to £2200 for an 8-day premium Iceland winter travel tour.
Ha: Customers are willing to pay more than £2200 for an 8-day premium Iceland winter travel tour.
Step 2: Identify all the factors in the z-score formula:
You can also calculate for the data set.
= 2366.67
Step 3: Use the z-score formula to calculate z-score.
Step 4 Use the Excel formula NORM.S.DIST(z, cumulative), to obtain a value that reflects the area right of z (p-value)
- Use the Excel formula ‘NORM.S.DIST(z, cumulative)’ and enter z = 2.24
- Set ‘cumulative’ to be TRUE
- Press ‘Enter’, and you will get the value that represents the area left of z equal to 0.9875
- The p-value = 1 − area left of z
- p-value = 0.0125
Step 5: Interpret the findings and decide whether to reject H0.
So far, you do not have enough information from the problem statement to make this decision. This is because the confidence level (or α) is unknown.
So, more specifically:
- If the company is looking for a 95% confidence level (α = 0.050), as the p-value (0.0125) is less than or equal to α, you will reject H0. This means that the marketing manager’s claim is true that ‘customers are willing to pay more than £2200 for an 8-day premium Iceland winter travel tour’.
- If the company is looking for a 99% confidence level (α = 0.010), as the p-value (0.0125) is greater than α, you will not reject H0. This means that the marketing manager’s claim that ‘customers are willing to pay more than £2200 for an 8-day premium Iceland winter travel tour’ is false.