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Data analysis: hypothesis testing
Data analysis: hypothesis testing

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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

Timing: Allow approximately 45 minutes to complete this activity

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.

Table 7 Customer responses
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.

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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.

mu equals 20

sigma equals 5.5

n equals 40

You can also calculate x macron for the data set.

x macron equals 21.45

Step 3: Use the z-score formula to calculate the z-score.

cap z equals 21.45 minus 20 divided by left parenthesis 5.5 divided by Square root of 40 right parenthesis

cap z equals 1.67

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.