6.4 Test your understanding
The following activity will test your understanding of how to calculate the p-value used to conduct a hypothesis test.
Activity 8 Determine p-value and testing hypothesis
Records show that customers are willing to pay less than or equal to £20 for a premium box of chocolate with a standard deviation of 5.5. A marketing manager believes that customers are willing to pay more than this. The marketing manager asks 40 customers how much they are willing to pay to test this belief. Table 7 shows the responses the marketing manager received from the 40 customers (in the value of £).
At the 95% confidence level, can you determine whether the marketing manager’s claim is true or false? You can copy-paste the data below into Excel to calculate the required variable(s) or use a calculator of your choice.
| 23 | 22 | 25 | 18 | 21 |
| 24 | 25 | 21 | 20 | 20 |
| 18 | 21 | 17 | 25 | 26 |
| 25 | 15 | 17 | 13 | 18 |
| 21 | 23 | 25 | 24 | 30 |
| 21 | 18 | 19 | 17 | 22 |
| 23 | 21 | 25 | 24 | 22 |
| 26 | 18 | 20 | 20 | 25 |
Use the free response box below to show your calculations.
Discussion
Step 1: Based on the information statements above, you can formulate the hypotheses:
H0: customers are willing to pay less than or equal to £20 for a premium box of chocolate.
Ha: customers are willing to pay more than £20 for a premium box of chocolate.
Step 2: Identify all the factors in the z-score formula.
You can also calculate for the data set.
Step 3: Use the z-score formula to calculate the 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).
When z = 1.67, p-value = 0.0475
Step 5: Interpret the findings and decide whether to reject H0.
You have been told the company is looking for a 95% confidence level (α = 0.050).
As the p-value (0.0475) 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 £20 for a premium box of chocolate’.
In conclusion, p-values are used in hypothesis testing to determine whether results are likely to be as extreme as the observed ones. The null hypothesis should be rejected in favour of the alternative hypothesis if the p-value is less than the significance level. In light of the evidence gathered from their study, managers can make informed decisions based on the p-value. They are able to determine whether their results are statistically significant or merely a result of chance based on their confidence in the results.