Question

to assess the accuracy of a laboratory scale, a standard weight that is known to weigh 1 gram is repeatedly weighed 4 times. the resulting measurements ( in grams) are : 0.95, 1.02, 1.01, 0.98. Assume that weighing by the scale when the true weight is 1 gram are normally distributed with mean u

a) use these data to compute a 95% confidence interval for u

B) do these data give evidence at 5% significance level that the scale is not accurate?
Answer this question by performing an appropriate test of hypothesis.

in order to ensure efficient usage of a server, it is necessary to estimate the mean number of concurrent users. According to records, the sample mean and sample standard deviation of number of concurrent users at 100 randomly selected times is 37.7 and 9.2, respectively.

A) construct a 90% confidence interval the mean number of concurrent users.

B) do these data provide significant evidence, at 1% significance level, that the mean number of concurrent is greater than 35?

Answer 1

a)

Given,

Confidence interval for population mean : (when population standard deviation is not known)

x : Measurements of weight : 0.95 , 1.02, 1.01, 0.98

Sample mean :

Sample standard deviation : s

Sample Mean :	0.99
Sample Standard Deviation : s	0.0316
Sample Size : n	4
Degrees of freedom : n-1	3
Confidence Level :	95
=(100-95)/100	0.05
/2	0.025
	3.1824

95% confidence interval for

95% confidence interval for = 0.9397, 1.0403

B).

Standard weight : Hypothesized mean : = 1 gm

Null hypothesis : Scale is accurate : H_o : =

Alternate Hypothesis : Scale is not accurate H_a :

Two Tailed test:

For Two tailed test :

As P-Value i.e. is greater than Level of significance i.e (P-value:0.5717 > 0.05:Level of significance); Fail to Reject Null Hypothesis
These data do not give significant evidence at 5% significance level that the scale is not accurate

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A)

Confidence interval for population mean : (when population standard deviation is not known)

Given
Sample Mean of number of concurrent users : :	37.7
Sample Standard Deviation of number of concurrent users : s	9.2
Sample Size : n	100
Degrees of freedom : n-1	99
Confidence Level :	90
=(100-90)/100	0.10
/2	0.05
	1.6604

90% confidence interval the mean number of concurrent users

90% confidence interval the mean number of concurrent users = (36.1724, 39.2276)

(B)

Hypothesize mean : = 35

Null hypothesis : H_o :

Alternate hypothesis : H_a :

Right tailed test.

For right tailed test :

As P-Value i.e. is less than Level of significance i.e (P-value:0.0021 < 0.01:Level of significance); Reject Null Hypothesis

These data do provide significant evidence, at 1% significance level, that the mean number of concurrent is greater than 35