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Data analysis: hypothesis testing
Data analysis: hypothesis testing

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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.

Table 6 Customers’ willingness to pay
£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:

cap z equals x bar minus mu divided by left parenthesis sigma divided by square root of n right parenthesis

mu equals 2200

sigma equals 500

n equals 45

You can also calculate x macron for the data set.

x macron = 2366.67

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

cap z equals 2366.67 minus 2200 divided by left parenthesis 500 divided by Square root of 45 right parenthesis

cap z equals 2.24

Step 4 Use the Excel formula NORM.S.DIST(z, cumulative), to obtain a value that reflects the area right of z (p-value)

  1. Use the Excel formula ‘NORM.S.DIST(z, cumulative)’ and enter z = 2.24
  2. Set ‘cumulative’ to be TRUE
  3. Press ‘Enter’, and you will get the value that represents the area left of z equal to 0.9875
  4. The p-value = 1 − area left of z
  5. 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.