To investigate the risk factors associated with developing gestational diabetes mellitus (GDM), 4320 women in the UK were monitored in a study from their twelfth week of pregnancy until delivery. Of these, 633 were diagnosed with GDM and the remaining 3687 were non-GDMs. One of the risk factors investigated was the age, in years, of the women. The sample mean age of the 633 women who developed GDM was 31.9 years with a sample standard deviation of 5.16 years. The sample mean and standard deviation of the ages of the 3687 non-GDM women were 30.36 years and 5.21 years respectively. (a) Show that it is appropriate to assume that the population variances are equal, and calculate the pooled estimate of the common population standard deviation. (b) A 95% confidence interval for the underlying difference between the mean age of women who develop GDM and non-GDM women was calculated to be (1.10, 1.98). Using this information what can you conclude about the difference in mean ages of the GDM and non-GDM women?

MATLAB: An Introduction with Applications
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To investigate the risk factors associated with developing gestational
diabetes mellitus (GDM), 4320 women in the UK were monitored in a
study from their twelfth week of pregnancy until delivery. Of these, 633
were diagnosed with GDM and the remaining 3687 were non-GDMs.
One of the risk factors investigated was the age, in years, of the women.
The sample mean age of the 633 women who developed GDM was
31.9 years with a sample standard deviation of 5.16 years. The sample
mean and standard deviation of the ages of the 3687 non-GDM women
were 30.36 years and 5.21 years respectively.
(a) Show that it is appropriate to assume that the population
variances are equal, and calculate the pooled estimate of the
common population standard deviation.
(b) A 95% confidence interval for the underlying difference between
the mean age of women who develop GDM and non-GDM women
was calculated to be (1.10, 1.98). Using this information what can
you conclude about the difference in mean ages of the GDM and
non-GDM women?
Transcribed Image Text:To investigate the risk factors associated with developing gestational diabetes mellitus (GDM), 4320 women in the UK were monitored in a study from their twelfth week of pregnancy until delivery. Of these, 633 were diagnosed with GDM and the remaining 3687 were non-GDMs. One of the risk factors investigated was the age, in years, of the women. The sample mean age of the 633 women who developed GDM was 31.9 years with a sample standard deviation of 5.16 years. The sample mean and standard deviation of the ages of the 3687 non-GDM women were 30.36 years and 5.21 years respectively. (a) Show that it is appropriate to assume that the population variances are equal, and calculate the pooled estimate of the common population standard deviation. (b) A 95% confidence interval for the underlying difference between the mean age of women who develop GDM and non-GDM women was calculated to be (1.10, 1.98). Using this information what can you conclude about the difference in mean ages of the GDM and non-GDM women?
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