Question

n a survey, 13 people were asked how much they spent on their child's last birthday gift. The results were roughly bell-shaped with a mean of $42 and standard deviation of $4. Construct a confidence interval at a 98% confidence level.

Give your answers to one decimal place.

Correct ±± Incorrect

Interpret your confidence interval in the context of this problem.

please do it step by step

thanks

Answer 1

The provided sample mean is Xˉ=$42 and the sample standard deviation is s=$4. The size of the sample is n = 13n=13 and the required confidence level is 98%.

The number of degrees of freedom are df=13−1=12, and the significance level is \alpha = 0.02α=0.02.

Based on the provided information, the critical t-value for α=0.02 and df=12 degrees of freedom is tc​=2.681.

The 98% confidence for the population mean \muμ is computed using the following expression

Therefore, based on the information provided, the 98 % confidence for the population mean \muμ is

CI= (42 - 2.974, 42 + 2.974)

CI=(39.026,44.974)

INTERPRETATION:

We are 98% confident that the population mean lies within the range 39.026< <44.974.

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