Question

Some dietitians have suggested that highly acidic diets can have an adverse affect on bone density in humans. Alkaline diets have been marketed to avoid or counteract this effect. Is the same thing true for cats, and would an alkaline diet be beneficial? Two groups of four cats were fed diets for 12 months that differed only in acidifying or alkalinizing properties. The bone mineral density (g/cm2) of each cat was measured at the end of 12 months. The summary statistics for bone mineral density appear in the table. Diet ? ?⎯⎯⎯ ? Acidifying 4 0.63 0.01 Alkalinizing 4 0.64 0.05 What conditions must be satisfied to justify the procedure used to find a 95% confidence interval for the mean bone mineral density of cats after 12 months on an acidifying diet?

very small randomized samples; also populations with uniform distributions

randomized and representative samples; also populations with Normal distributions

The samples need to be representative; this alone meets the conditions.

The populations only need to be Normally distributed.

What conditions must be satisfied to justify the test used to see if there is strong evidence that cats on an alkalinizing diet have higher mean bone mineral density after 12 months than cats on an acidifying diet?

The populations only need to be Normally distributed.

very small randomized samples; also populations with uniform distributions

The samples need to be representative; this alone meets the conditions.

randomized and representative samples; also populations with Normal distributions

What conditions must be satisfied to justify the procedure used to find a 95% confidence interval for the difference in mean bone mineral density after 12 months on an alkalinizing diet and an acidifying diet?

The samples need to be representative; this alone meets the conditions.

randomized and representative samples; also populations with Normal distributions

very small randomized samples; also populations with uniform distributions

The populations only need to be Normally distributed.

Answer 1

Answer:

CI for mean:-

The confidence interval of the mean of a measurement variable is commonly estimated on the assumption that the statistic follows a normal distribution, and that the variance is therefore independent of the mean. This is known as a normal approximation confidence interval.

Hence;

            “The populations only need to be normally distributed.”

Test for Mean difference:-

In order to test whether there is a difference between population means, we are going to make three assumptions:

1. The two populations have the same variance. This assumption is called the assumption of homogeneity of variance.

2. The populations are normally distributed.

3. Each value is sample independently from each other value.

Hence;

            “Randomized and representative samples also populations with normal distribution.”

CI for difference of Mean:-

In order to construct a confidence interval, we are going to make three assumptions:

1. The two populations have the same variance. This assumption is called the assumption of homogeneity of variance.

2. The populations are normally distributed.

3. Each value is sampled independently from each other value.

Hence;

            “Randomized and representative samples also populations with normal distribution.”

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