Question

Using the following stock data for GRMN and LMT, Answer the following questions. (Show Work).

Stock GRMN LMT Mean 100.05 99.79 Standard Deviation 1.10 1.47 Sample Size 62 62

a. Calculate the 95% two-sample confidence interval. What can be determined from this confidence interval. Is the difference in stock price significantly different from 0?

b. Conduct a two-sample t-test using an alpha value of 0.05.

c. If there was a significant difference between GRMN and LMT, What is the probability of making a Type I error?

Answer 1

Solution:-

a) 95% two-sample confidence interval is C.I = (-0.2017, 0.7217).

C.I = 0.26 + 1.98 × 0.23317

C.I = 0.26 + 0.4617

C.I = (- 0.2017, 0.7217)

No the difference in stock price is not significantly different from 0.

b)

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

Null hypothesis: u₁ = u ₂
Alternative hypothesis: u₁ u ₂

Note that these hypotheses constitute a two-tailed test.  

Formulate an analysis plan. For this analysis, the significance level is 0.05. Using sample data, we will conduct a two-sample t-test of the null hypothesis.

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

SE = sqrt[(s₁²/n₁) + (s₂²/n₂)]
SE = 0.23317
DF = 122
t = [ (x₁ - x₂) - d ] / SE

t = 1.12

where s₁ is the standard deviation of sample 1, s₂ is the standard deviation of sample 2, n₁ is the size of sample 1, n₂ is the size of sample 2, x₁ is the mean of sample 1, x₂ is the mean of sample 2, d is the hypothesized difference between the population means, and SE is the standard error.

Since we have a two-tailed test, the P-value is the probability that a t statistic having 122 degrees of freedom is more extreme than -1.12; that is, less than -1.12 or greater than 1.12.

Thus, the P-value = 0.265

Interpret results. Since the P-value (0.265) is greater than the significance level (0.05), we have to accept the null hypothesis.

c) From the above test we have sufficient evidence in the favor of the claim that there is no significance difference in stock price.