Question

URGENT!!!
Can you please solve this example in 50 minutes.

The variance for duration of a telephone conversation is 1.6 minutes². From the records about telephone conversations, the average duration of conversations should be examined on the basis of a random sample of 10 conversations. Average in sample was 2 minutes. Determine the limits for which can be expected to cover the average duration of the conversation. The first type error is 1%.

a)    In this example we should estimate:

a.     Confidence interval for population total

b.    Confidence interval for mean, known population variance

c.     Confidence interval for standard deviation, small sample

d.    Confidence interval for mean, unknown population variance, small sample

b)    For confidence interval construction, theoretical value according to appropriate theoretical probability distribution is _______.

c)    Standard error (or estimation for standard error) for confidence interval construction is ­­­­­­_________.

d)    Lower limit for confidence interval is ________ minutes.

e)    Upper limit for confidence interval is ________ minutes.

Answer 1

(a).

In this example we should estimate confidence interval for mean, known population variance as the variance for duration of a telephone conversation is 1.6 minutes which is specified in the study.

Hence the correct option is b.

(b).

The first type error is 1% which means alpha is 0.01.

The significance level 0.01 implies the 99% confidence interval.

At the significance level 0.01, the two-tailed critical value obtained from z-table is +/- 2.58.

Therefore, for the construction of 99% confidence interval, theoretical value according to appropriate theoretical probability distribution is +/- 2.58.

(c).

The variance is 1.6 minutes.

So, the population standard deviation,

Therefore, the standard error (or estimation for standard error) for confidence interval construction is,

Therefore, standard error (or estimation for standard error) for confidence interval construction is 0.40 minutes.

d).

The lower limit for 99% confidence interval is,

Therefore, the lower limit is 0.968 minutes.

e).

The upper limit for 99% confidence interval is,

Therefore, the upper limit is 3.032 minutes.