rfvhh A company produces precision 1 meter 1000 mm rules The

A company produces precision 1 meter (1000 mm) rules. The actual distribution of lengths of the rules produced by this company is national with mean mu and standard deviation 20 mm.

Solution

15)

Here in the 15th question we are given four data points.

1000.01 999.98 1000 1000.01

90% confidence interval for mu is,

Xbar - E < mu < Xbar + E

n = number of data points = 4

Xbar = mean of the observations = sum of observations / total number of observations = 1000

s = standard deviation of the data = (x - mean)² / n-1 = 0.01414

E is the margin of error = tc * s / sqrt(n)

where tc is the critical value for t distribution

By using table for t-distribution,

tc = 1.638

E = (1.638 * 0.01414) / sqrt(4) = 0.0115

90% confidence interval for mu is,

1000.00 + or - 0.0115

option b) is correct.

16) Here the 95% confidence interval for mean is 1.33 to 5.27.

And test of the hypothesis is,

H0 : mu = 5 Vs H1 : mu 5

Here population mean is lie in the confidnce interval so we accept the null hypothesis.

that is option b) is correct

I would not reject H0 at level 0.05 .

17) In a statistical test of hypothesis we say that the data are statistically significant at level if P-value is less than .

Option c) is correct.

18) Given that P-value = 0.038

We say that result is significant if P-value < (level of significane)

Here in the third option given that the 0.05 level but not at the 0.01 level.

That means for is 0.05 ,

P-value (0.038) < (0.05)

And for is 0.01 ,

P-value not less than

So option c) is correct.

So the result is statistically significant at 0.05 but not at 0.01 level.

19) Means of random samples are less variable than individual observations.