Question

Fasting concentrations (mmol/L) of glucose in blood were measured in a sample of diabetic patients implanted with a new insulin delivery platform.

P#1	P#2	P#3	P#4	P#5	P#6	P#7	P#8	P#9	P#10
5.5	4.8	3.8	4.0	5.2	5.1	4.8	4.4	4.2	6.1

Computer simulations of the platform predicted a fasting glucose level of 4.5 mmol/L.

Use a statistical test to fundament your opinion on whether the data is consistent with the model prediction.

1. Identify suitable null and alternative hypotheses.
2. Is a t-test is suitable for this problem. Why?
3. Calculate critical values for a significance level of 0.01. Is the data is consistent with the computer model? Justify
4. Calculate p-value. Is the data is consistent with the computer model? Justify.

Answer 1

(a)

H0: Null Hypothesis: = 4.5

HA: Alternative Hypothesis: 4.5

(b)

t - test is suitable for this problem, because:

(i) The dependent variable is continuous.

(ii) The observations are independent of one another

(iii) The dependent variable should be approximately normally distributed - Though this condition is not explicitly stated, the same can be assumed.

(iv) The dependent variable does not contain outliers.

(c)

= 0.01

ndf = n - 1 = 10 - 1 = 9

From Table, critical values of t = 3.2498

From the given data the following statistics are calculated:

n = 10

= 4.79

s =0.7141

SE = s/

= 0.7141/= 0.2258

Test statistic is:

t = (4.79 -4.5)/0.2258 = 1.28

Since the calculated value of t = 1.28 is less than critical value of t = 3.2498, the difference is not significant. Fail to reject null hypothesis.

Conclusion: The data is consistent with the computer model.

(d)

t score = 1.28

ndf = 9

Two Tail test

By Technology, p - value= 0.2326

Since p - value = 0.2326 is greater than = 0.01, the difference is not significant. Fail to reject null hypothesis.

Conclusion: The data is consistent with the computer model.