Question

# A group of researchers developed a 95% z confidence interval for the mean body mass index...

A group of researchers developed a 95% z confidence interval for the mean body mass index (BMI) of women aged 20 to 29 years, based on a national random sample of 647 such women. They assumed that the population standard deviation was known to be σ = 7.5. In fact, the sample data had mean BMI x = 26.9 and standard deviation s = 7.39. What is the 95% t confidence interval for the mean BMI of all young women? (Round your answers to three decimal places.)

The provided sample mean is and the sample standard deviation is s=7.39. The size of the sample is n=647 and the required confidence level is 95%.

The number of degrees of freedom are df=647−1=646, and the significance level is α=0.05.

Based on the provided information, the critical t-value for α=0.05 and df=646 degrees of freedom is tc​=1.964.

The 95% confidence for the population mean \muμ is computed using the following expression

Therefore, based on the information provided, the 95 % confidence for the population mean μ is

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