Suppose that a group of 100 consumers are asked to rate how much they liked the taste of a new soft drink on a 5-point scale (where 5 = good taste and 1 = poor taste). The mean rating was 4.6, with a standard deviation of 1.25. Suppose, further, that the standard error of the mean for this study was 0.15. If you wanted to find the 95 per cent confidence interval (two-tailed test), and if the Z-value at the .05 level of significance is 1.96, then the confidence interval lies between approximately:
A) 4.45 and 4.75.
B) 4.31 and 4.89.
C) 4.36 and 4.85.
D) 4.57 and 4.63.

Question

Quizplus · Accepted Answer

To calculate the confidence interval, we use the formula:

CI = X̄ ± Z*(SE)

Where X̄ is the sample mean, Z is the Z-value at the desired level of significance (1.96 for a 95% confidence level), and SE is the standard error of the mean.

Plugging in the values from the problem, we get:

CI = 4.6 ± 1.96*(0.15)
CI = 4.6 ± 0.294
CI = [4.306, 4.894]

Rounded to two decimal places, the confidence interval is [4.36, 4.85]. Therefore, the best choice is C.

Suppose That a Group of 100 Consumers Are Asked to Rate