Question

The experimenter examines thought processes and had 10 kids eat as many lollipops as they could in ten minutes. Group 1 was told that this tested innate eating ability, group 2 was told this was a task to fill time. Data:

Innate eating ability:   4, 7,6, 5, 8,

Time-filling eating ability:   8, 9,11, 5, 9,

a)Tell me if there's a difference in the means for the two groups? Use a significance level of .05 for this question

b)You'll assume, in the population, you could believe that number of lollipops eaten is normally distributed. You can also assume that the variances are equal. Given these assumptions, compute the appropriate test statistic to test the null hypothesis.

c) What's the decision rule for making a decision about the null hypothesis?What is the critical value(s) that would be used for this problem?

d) What is the decision regarding the null hypothesis?

e) interpret the results

Answer 1

For innate eating ability

= 6, s1 = 1.581, n1 = 5

For time-filling eating ability

= 8.4, s2 = 2.191, n2 = 5

H₀: 

H₁:

The pooled variance(s_p²) = ((n1 - 1)s1^2 + (n2 - 1)s2^2)/(n1 + n2 - 2) = (4 * (1.581)^2 + 4 * (2.191)^2)/(5 + 5 - 2) = 3.65

The test statistic t = ()/sqrt(s_p²/n1 + s_p²/n2)

= (6 - 8.4)/sqrt(3.65/5 + 3.65/5)

= -1.986

df = 5 + 5 - 2 = 8

At = 0.05, the critical values are +/- t_{0.025, 8} = +/- 2.306

Since the test statistic value is not less than the negative critical value (-1.986 > -2.306), so we should not reject the null hypothesis.

At 0.05 significance level there is not sufficient evidence to conclude that there is a significant difference in the means for the two groups.