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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?

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?

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN:9780079039897
Author:Carter
Publisher:Carter
Chapter10: Statistics
Section10.3: Measures Of Spread
Problem 1GP
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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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