Apaint manufacturer wishes to compare the drying times of two different types of paint. independent random samples of 11 cans of type a and 9 cans of type b were selected and applied to similar surfaces. the drying times (in hours) were recorded. the summary statistics are as follows. type a type b mean 76.8 hours 66.1 hours standard deviation 4.5 hours 5.1 hours sample size 11 9 construct a 95% confidence interval for the difference between the mean drying time for all type a paint and type b paint. the degree of freedom that is used for the construction of this 95% confidence interval is

Size of the first sample n_1=11

Size of the second sample n_2=9

Mean of the first sample \bar{x_1}=76.8

Mean of the second sample \bar{x_2}=66.1

Standard deviation of the first sample s_1=4.5

Standard deviation of the second sample s_2=5.1

Null Hypotheis: \mu_1=\mu_2 [mean drying time is same for two types]

Alternate Hypothesis:

The test statistics:

Using the "Test for equality of two means"

}=4.91939 " alt=" (76.8-66.1)\pm1.96(\sqrt{\frac{4.5^2}{11}+\frac{5.1^2}{9}})" />}=4.91939 " />

Thus the calculated value is |z|=4.9194

Table value at 5% level of significance is 1.96.

Here the table value 1.96 is less than the calculated value. Thus we rejected H_0 at 5% level.

The 95% confidence interval for