Respuesta :
Using the t-distribution, the 90% confidence interval for the number of chocolate chips per cookie for Big Chip cookies is (8.374, 9.426).
What is a t-distribution confidence interval?
The confidence interval is:
[tex]\overline{x} \pm t\frac{s}{\sqrt{n}}[/tex]
In which:
- [tex]\overline{x}[/tex] is the sample mean.
- t is the critical value.
- n is the sample size.
- s is the standard deviation for the sample.
The critical value, using a t-distribution calculator, for a two-tailed 90% confidence interval, with 76 - 1 = 75 df, is t = 1.9921.
The other parameters are given as follows:
[tex]\overline{x} = 8.9, s = 2.3, n = 76[/tex].
Hence the bounds of the interval are:
[tex]\overline{x} - t\frac{s}{\sqrt{n}} = 8.9 - 1.9921\frac{2.3}{\sqrt{76}} = 8.374[/tex]
[tex]\overline{x} + t\frac{s}{\sqrt{n}} = 8.9 + 1.9921\frac{2.3}{\sqrt{76}} = 9.426[/tex]
More can be learned about the t-distribution at https://brainly.com/question/16162795
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