Suppose a researcher is interested in the relationship between BMI (kg/m2) and f

Question

Suppose a researcher is interested in the relationship between BMI (kg/m2) and fasting glucose levels (mg/dL). The researcher is conducting a cross-sectional study with prevalent data in order to quantify the relationship in the greater population. In order to do so, the researcher plans to conduct a formal hypothesis test. The following table includes measurements for both BMI and fasting glucose in a SRS of individuals. Write out your null and alternative hypotheses. Assuming all necessary conditions are met, carry out a formal test to determine if there is a correlation between BMI and fasting glucose. Interpret your p-value.

BMI (kg/m2)

Fasting Glucose (mg/dL)

32.4

112

29.7

116

31.5

114

32.1

117

30.2

114

30.4

113

Ans:

Ho: =0 Ha:0

t statistic =b/SEb= -0.315 pvalue=0.768

We fail to reject the Ho that there is no linear relationship between the two variables

Please give me the detailed and complete process of solving this problem.

BMI (kg/m2)

Fasting Glucose (mg/dL)

32.4

112

29.7

116

31.5

114

32.1

117

30.2

114

30.4

113

Explanation / Answer

test statistic = b /se (b) = -0.262510254/0.832909 = -0.31517

p-value = 2 P(t < -0.31517) = 0.76838

we fail to reject the null hypothesissince p-value = 0.768 > 0.05 {level of significance}

SUMMARY OUTPUT Regression Statistics Multiple R 0.155665397 R Square 0.024231716 Adjusted R Square -0.219710355 Standard Error 2.056290162 Observations 6 ANOVA df SS MS F Significance F Regression 1 0.420016 0.420016 0.099334 0.768388 Residual 4 16.91332 4.228329 Total 5 17.33333 Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Lower 95.0% Upper 95.0% Intercept 122.4842767 25.87544 4.73361 0.00908 50.64252 194.326 50.64252 194.326029 X Variable 1 -0.262510254 0.832909 -0.31517 0.768388 -2.57504 2.050016 -2.57504 2.050015797

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