Question

Below is a sample of 25 exam scores.

80 79 69 71 74 73 77 75 65 52 81 84 84 79 70 78 62 77 68 77 88 70 75 85 84

1. Is the exam score significantly greater than 70 at the 5 percent level of significance? Follow and show the 7 steps for hypothesis testing.

2. Determine the p-value and interpret its meaning.

3. What assumption must you make about the population distribution in order to conduct the test in part a? Is the assumption valid? Use and include an appropriate graph from Minitab. Write a couple of sentences supporting your answer.

4. Verify your results (in parts a and b) using Minitab.

Answer 1

Solution:-

1)

State the hypotheses. The first step is to state the null hypothesis and an alternative hypothesis.

Null hypothesis: u < 70
Alternative hypothesis: u > 70

Note that these hypotheses constitute a one-tailed test.

Formulate an analysis plan. For this analysis, the significance level is 0.05. The test method is a one-sample t-test.

Analyze sample data. Using sample data, we compute the standard error (SE), degrees of freedom (DF), and the t statistic test statistic (t).

SE = s / sqrt(n)

S.E = 1.6227
DF = n - 1

D.F = 24
t = (x - u) / SE

t = 3.13

t_critical = 1.711

Rejection region is t > 1.711.

where s is the standard deviation of the sample, x is the sample mean, u is the hypothesized population mean, and n is the sample size.

The observed sample mean produced a t statistic test statistic of 3.13.

Interpret results. Since the t-value (3.13) lies in the rejection region, hence we have to reject the null hypothesis.

From the above test we have sufficient evidence in the favor of the claim that exam score significantly greater than 70.

2)

Thus the P-value in this analysis is 0.002.

Interpret results. Since the P-value (0.002) is less than the significance level (0.05), we have to reject the null hypothesis.

3) The assumption we must make about the population distribution in order to conduct the test in part a are:-

The population from which sample is taken is assumed to be normally distributed.

The sample is random sample.

Sample size is large enough.

Yes, the assumption is valid.