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Ludmilka [50]
3 years ago
15

A local company makes a candy that is supposed to weigh 1.00 ounces. A random sample of 25 pieces of candy produces a mean of 0.

996 ounces with a standard deviation of 0.004 ounces. Construct a 98 percent confidence interval for the mean weight of all such candy. Assume that X, the weight of a candy, is distributed normally.
Mathematics
1 answer:
Firlakuza [10]3 years ago
6 0

Answer: (0.994, 0.998)

Step-by-step explanation:

Given : Sample size : n= 25 < 30 , so we use t-test.

\overline{x}=0.996\ \ ;\ s=0.004

Critical t-value use for 98% confidence :

t_{n-1,\alpha/2}=t_{24,0.01}=2.492

Formula to find the confidence interval :-

\overline{x}\pm t_{\alpha/2}(\dfrac{\sigma}{\sqrt{n}})

i.e. 0.996\pm (2.492)(\dfrac{0.004}{\sqrt{25}})

=0.996\pm 0.0019936\approx0.996\pm0.002\\\\=(0.996-0.002,\ 0.996+0.002)\\\\=(0.994,\ 0.998)

Hence, the required confidence interval : (0.994, 0.998)

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