21. In an attempt to compare the durability of two different materials (X and Y), 10 pieces of ?type X and 14 pieces of type Y were used. From these samples we calculate the statistics: x? = ??129.44, ? = 122.65, sx = 9.15, sy = 11.02. The pooled estimate of the standard deviation, sp, in the two-sample test statistic is: ? *

?10.30?

?106.01?

?10.28?

?105.72?

?22. In an attempt to compare the durability of two different materials (X and Y), 10 pieces of ?type X and 14 pieces of type Y were used. From these samples we calculate the statistics: x? = ??129.44, ? = 122.65, sx = 9.15, sy = 11.02. Assuming the two populations sampled are normal with equal variance, find the P-value. ? *

?(0.1, 0.2)?

?(0.01, 0.025)?

?(0.05, 0.10)?

?(0.02, 0.05).?

?23. Two methods A and B, were used to find the latent heat of fusion of ice. 13 measurements ?were made with method A and 8 measurements were made with method B with statistics: x?A = ??80.02, x?B = 79.98,sA = 0.024 and sB = 0.031. To test equal means assuming normality and equal ?variances, the observed test statistic (to 1dp) and the P-value are: ? *

Test statistics = 1.2; P-value = P(|t19| > 1.2) > 0.2?

Test statistics = 3.3; P-value = P(t19 > 3.3)

Test statistics = 3.3; P-value = P(t21 > 3.3)

Test statistics = 3.3; P-value = P(|t19| > 3.3)

?24. A recent study showed that 53% of university applications were submitted on campus. ?Assume that this result is based on a simple random sample of 1,000 applications, with 530 ?submitted on campus. Use a 0.01 significance level to test the claim that among all applications ?the percentage submitted on campus is equal to 50%. The final decision is:? *

There is not sufficient evidence to warrant rejection of the claim that the percentage of ?university applications submitted on campus is equal to 50%. ?

There is not sufficient sample evidence to support the claim that the percentage of university ?applications submitted on campus is equal to 50%. ?

There is sufficient evidence to warrant rejection of the claim that the percentage of university ?applications submitted on campus is equal to 50%.?

The sample data support the claim that the percentage of applications submitted on campus is ?equal to 50%. ?

?25. The average amount of time men and women spend practicing meditation in Nepal resort ?each week is believed to be the same. A study is done and data are collected, resulting in the ?data in the table below. Each population has a normal distribution. Is there a difference in the ?mean amount of time men and women practice meditation every week? Test at the 5% level of ?significance.(populations standard deviations are assumed unequal).? *

Average Number of Sample Size Hours Practicing Sample Standard meditation Per week Deviation Women 9 2 0.866 Men 16 3.2 1,0