Question

In: Statistics and Probability

A busy pharmacy has a BMI weight scale installed inside the pharmacy, which is available to...

A busy pharmacy has a BMI weight scale installed inside the pharmacy, which is available to customers from Monday through Friday when the pharmacy is open for business. The manager of the pharmacy wanted to investigate if the number of persons utilizing the BMI scale are the same for each of the 5 days of the week. To investigate this, the manager randomly selected one week and counted the number of customers who used the scale on each of the 5 days during this week. The table below presents the information obtained.

Day

Monday

Tuesday

Wednesday

Thursday

Friday

Number of customers

260

199

215

299

286

At the 5% level of significance, should the researcher for the pharmacy reject the null hypothesis that the number of customer who use the BMI scale each of the 5 days of the week is the same?

Conduct a goodness of fit test for this above information, using the steps for hypothesis testing below.                          

  1. Null and alternative hypotheses
  2. Level of significance
  3. Test statistics
  4. Critical values and rejection region
  5. Process of checking to see whether the test statistic falls in the rejection region
  6. Conclusion in words

Solutions

Expert Solution

Solve using Excel:

Day No. of cusomers Observed proportion(O) Expected proportion (E) (Oi - Ei)2 / Ei
Monday 260 0.207 0.20 0.0002
Tuesday 199 0.158 0.20 0.0088
Wednesday 215 0.171 0.20 0.0043
Thursday 299 0.237 0.20 0.0070
Friday 286 0.227 0.20 0.0037
Total 1259 Test statistic 0.0133
Day No. of cusomers Observed proportion(O) Expected proportion (E) (Oi - Ei)2 / Ei
Monday 260 =B2/1259 =1/5 =(C2-D2)^2/D2
Tuesday 199 =B3/1259 =1/5 =(C3-D3)^2/D3
Wednesday 215 =B4/1259 =1/5 =(C4-D4)^2/D4
Thursday 299 =B5/1259 =1/5 =(C5-D5)^2/D5
Friday 286 =B6/1259 =1/5 =(C6-D6)^2/D6
Total =SUM(B2:B6) Test statistic =SUM(E2:E4)

a. H0: p1 = p2 = p3 = p4 = p5, Number of customer who use the BMI scale each of the 5 days of the week is the same

H1: At least one pi is different, Number of customer who use the BMI scale each of the 5 days of the week is not the same

b. Level of significance = 0.05

c. Test statistic: χ2 = 0.013

d. Degrees of freedom: df = k-1 = 5-1 = 4

Left-tail critical value (Using Excel CHISQ.INV(probability,df)) = CHISQ.INV(0.05,4) = 0.711

Right-tail critical value (Using Excel CHISQ.INV.RT(probability,df)) = CHISQ.INV.RT(0.05,4) = 9.488

Rejection Region: Reject H0 if -χ2 < 0.711 or χ2 > 9.488

e. Since test statistic (0.013) is less than critical value (9.488), we do not reject the null hypothesis.

f. Conclusion: Number of customer who use the BMI scale each of the 5 days of the week is not the same.


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