A 95% confidence interval for the difference in mean sugar content between adult cereals (μ1) and children's cereals (μ2)

was found to be (-40.5, -33.6) grams.

Provide an appropriate interpretation of this interval, then use it to explain which type of cereal (adult or children's) appears to have the higher mean sugar content.

 

We are 95% confident that the true population difference in mean sugar content between adult cereals and children's cereals is between -40.5 and -33.6 grams.

The cereal with a higher mean sugar content is the children's cereals (μ2). This is because, the confidence interval is negative meaning that since μ1 - μ2 is negative, μ2 must be larger than μ1.

Step-by-step explanation

Confidence interval indicates the level of confidence we have that the true population parameter is within the interval. Therefore we shall have it as; We are 95% confident that the true population difference in mean sugar content between adult cereals and children's cereals is between -40.5 and -33.6 grams.

The cereal with a higher mean sugar content is the children's cereals (μ2). This is because, the confidence interval is negative meaning that since μ1 - μ2 is negative, μ2 must be larger than μ1.