Question

This mentis p er due du 12/09/2019 115 . You wa Due Wed 12/11/2011 The bow shows the mind that the same Domast the m ount of time on wag thanh treh Rats 28, 29, 29, 25, 27, 30, 3 28 Hamster: 27, 50, 21, 32, 33, 31, 4 19 4 20 Assume that both populations follow altistribution. What can be conclude For this maty, we should we Select on 2. The mall and heative hypotheses would be the l e vel o f .: Secr t N: Eestrower DEG The test - please show your ser decimal places) c. The (Peshow your wer to decimal places) d. The p-value e. Based on this we should be the bull lyphesis Thus, the final conclusion is that... There are all insignificant at 0.05, so there is insuficient de te conclude that the time to complete resistente pe Thermals are w cally significant 0.05, so there is evidence conclude that the population mente e complete the area is the The results are statically insignificant -0.05, so there is statistically significant evidence to conclude that the population meminte complete the form is the pe o ple The results we stay at 0.05, so there is sufficient evidence to conclude that the time to come the more for the time is the same as the c r ew 3. Interpret the p-value is the context of the study There is a 11.54% chance of a Type leme There is a 11.54% chance that the mesme to complete the m othe r by scored the meant to let me the 10 If the umple meaning to complete them for the resiste me the sample meantime complete the h an n o real them the w a lls mean time to complete the more for the riders by at least 6.1 seconds compared to the time to complete them for the 10 homes If the population time to complete the mare for t he same as the population time to complete them for hamster and there and w e were then there has chance the complete de mare de sus dat by l e d to the meant to them the 10 Terpret the level of significance in the of the study If the population mean time to complete the more forma is the same as the propo s e to the m or nind the 10t h , then there w a s and same completed oncluding the for th d 10 dimechober I put me to compleme the more feats in the same as the population met t e in and thered 10 meserved then there would beache d concluding the the population m i t eplete them for at both the population mano complete the man for har There is a chance that will them There is a is the same chance that the population mean time to replete the mare for and that the they

Answer 1

Solution:-

We will conduct a two-sample t-test of the null hypothesis.

a)

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

Null hypothesis: u₁ = u ₂
Alternative hypothesis: u₁$\neq$ u₂

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).

Rats Sum Mean S.D Count Hamsters 270 361 36.1 5.4772255750 9.9493160010 10 S.E 1.8257418583 3.1462499724

SE = sqrt[(s₁²/n₁) + (s₂²/n₂)]
SE = 3.637
DF = 17
b)

t = [ (x₁ - x₂) - d ] / SE

t = - 1.68

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 17 degrees of freedom is more extreme than -1.68; that is, less than -1.68 or greater than 1.68.

c)

Thus, the P-value = 0.1154.

d) Interpret results. Since the P-value (0.1154) is greater than the significance level (0.05), e) hence we should fail to reject the null hypothesis.

f) The results are statistically insignificant at alpha = 0.05, so there is insufficient evidence to conclude that the population mean to complete the maze for rat is not same as the population mean to complete the maze for hamsters.

g) If population mean time to complete the maze for rats is the same as the population mean time to complete the maze for the hamsters and if another 9 rats and 10 hamsters are observed than there would be 11.54% chance that the mean time to complete the maze for the 9 rats would differ by at-least 6.1 seconds compared to mean time to complete the maze for the 10 hamsters