A random sample of 11 nursing students from Group 1 resulted in a mean score of 41.3 with a standard deviation of 6.8. A random sample of 14 nursing students from Group 2 resulted in a mean score of 54.8 with a standard deviation of 6. Can you conclude that the mean score for Group 1 is significantly lower than the mean score for Group 2? Let μ1 represent the mean score for Group 1 and μ2 represent the mean score for Group 2. Use a significance level of α=0.1 for the test. Assume that the population variances are equal and that the two populations are normally distributed.

Question

Mathematics

Odin

13 September, 10:49

A random sample of 11 nursing students from Group 1 resulted in a mean score of 41.3 with a standard deviation of 6.8. A random sample of 14 nursing students from Group 2 resulted in a mean score of 54.8 with a standard deviation of 6. Can you conclude that the mean score for Group 1 is significantly lower than the mean score for Group 2? Let μ1 represent the mean score for Group 1 and μ2 represent the mean score for Group 2. Use a significance level of α=0.1 for the test. Assume that the population variances are equal and that the two populations are normally distributed.

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Amara Schmidt · Answer 1

At 1% significance level, this difference is considered to be extremely statistically significant.

Step-by-step explanation:

Group Group One Group Two

Mean 41.300 54.800

SD 6.800 6.000

SEM 2.050 1.604

N 11 14

H0: Mean of group I = Mean of group II

Ha: Mean of group I < mean of group II

(Left tailed test at 1% significance level)

The mean of Group One minus Group Two equals - 13.500

standard error of difference = 2.563

t = 5.2681

df = 23

p value = 0.00005

Since p < significance level, reject H0