Question

In: Statistics and Probability

For each of the following, (a) state the null hypothesis and (b) state the alternate hypothesis,...

For each of the following, (a) state the null hypothesis and (b) state the alternate hypothesis, (c) state the type of test that you will use to test the hypothesis and the level of significance, (d) state the critical value , (e) calculate the z-statistic or the t-statistic, (f) state whether we shall reject or fail to reject the null hypothesis, (g) state the relation between the p-value and α with an appropriate inequality, and (h) conclude the hypothesis test with an appropriate summarizing statement addressing the alternate hypothesis.

  1. Rosie is an aging cocker spaniel in Elkin, NC who gets regular check-ups from her owner, the local veterinarian. Let x be a random variable that represents Rosie’s resting heart rate (in beats per minute). The vet checked the Merck Veterinary Manual and found for dogs of this breed, μ = 115 beats per minute. Over the past six weeks, Rosie’s heart rate in beats per minute measured 93, 109, 110, 89, 112, and 117. The vet is concerned that Rosie’s heart rate may be slowing. At the α = 0.01 level of significance, do the data indicate that this is the case? A normal probability plot shows the data to have a linear correlation of 0.938. A box-and-whiskers plot of the data shows no outliers.

  1. In 1990, 23.8% of the 18- to 24-year old population of Finy Beach was attending college. This year, a random sample of 610 Finy Beach residents in the age group indicated showed that 178 were attending college. Do these data indicate that the population proportion of the 18- to 2y-year olds in Finy Beach who are attending college is different from 23.8%? Test the claim using α = 0.05.

Solutions

Expert Solution

1) The null hypothesis is Ho : mu >=115

Ha : mu < 115

Level of significance is 5% and test is one sided.

Test statistic is t = n1/2 *(Xbar - mu) /s with degree of freedom n-1

X bar = sample mean = 105 (calculated)

n = sample size = 6

s = sample standard deviation = 11.26 ( calculated with df =5)

Calculated value of t = -10* 2.449 / 11.26 = -2.17

The mod of this value is 2.17

The pvalue is 0.041072

The Critical value of t is calculated with degree of freedom =5 and alpha =0.05 This is found to be 2.015 (from t table)

As mod calculated t > t tabulated we reject the null hypothesis

Also as p < level of significance (0.041072 <5) we reject the null hypothesis

Hence we conclude that there is a significant slowing in the heart beat of the cocker spaniel.

2) Here Ho : P =0.238

Ha : p is not equal to 0.238

Level of significance is 5% (two sided)

Test statistic is Z = p-P /(PQ/n)1/2

where p = sample proportion = 178/610 = 0.291

P = population proportion = 0.238

Q= 1-P =0.762

n= 610

Putting this we get Z =3.08

Critical value of Z is 1.96 (corresponding to right tail of 2.5%)

p value of getting a Z score of 3.06 is 0.00207

Hence as Zcalc > Z tab we reject the null hypothesis

Also as p < 2.5% we reject the null hypothesis

We thus conclude that the proportion is significantly different form 23.8%


Related Solutions

For each of the following, (a) state the null hypothesis and (b) state the alternate hypothesis,...
For each of the following, (a) state the null hypothesis and (b) state the alternate hypothesis, (c) state the type of test that you will use to test the hypothesis and the level of significance, (d) state the critical value , (e) calculate the z-statistic or the t-statistic, (f) state whether we shall reject or fail to reject the null hypothesis, (g) state the relation between the p-value and α with an appropriate inequality, and (h) conclude the hypothesis test...
(2) 1. Can the null hypothesis or the alternate hypothesis state that the mean of the...
(2) 1. Can the null hypothesis or the alternate hypothesis state that the mean of the population is equal to a value? Explain. (2) 2. If the null hypothesis is that the mean is less than or equal to 4, what is the alternate hypothesis? (2) 3. What is the power of the test? Explain what beta is. (2) 4. Explain the difference between a type I and a type II error. (2) 5. Can you use both Tchebysheff's Rule...
State the null hypothesis. State the alternate hypothesis. What is (are) the independent variable(s)? What is...
State the null hypothesis. State the alternate hypothesis. What is (are) the independent variable(s)? What is (are) the dependent variable(s)? Objective African-American adolescents are twice as likely to develop hypertension in early adulthood than adolescents from other racial groups. The purpose of this study was to determine the efficacy of a school-based health promotion intervention. Method Participants were African-American adolescents aged between 14 and 17 years attending an urban high school. The 9-week intervention program focused on the participants' knowledge,...
Some of the statements below refer to the null hypothesis, some to the alternate hypothesis. State...
Some of the statements below refer to the null hypothesis, some to the alternate hypothesis. State the null hypothesis, H0, and the alternative hypothesis, Ha, in terms of the appropriate parameter (μ or p). A. The mean number of years Americans work before retiring is 34. (out of the following) H0: p = 34,     Ha: p ≠ 34 H0: μ = 34,     Ha: μ ≠ 34      H0: p ≥ 34,     Ha: p < 34 H0: p ≤ 34,     Ha: p > 34 H0: μ...
a. State the null and alternate hypothesis, and state the claim/Draw the Bell curve and shade...
a. State the null and alternate hypothesis, and state the claim/Draw the Bell curve and shade the appropriate tail b. State the Critical value c.. Compute the test value d. State the decision e. Conclusion 4. A machine that fills beverage cans is supposed to put 16 ounces of beverage in each can. Following are the amounts measured in a simple random sample of eight cans. Assume that the sample is approximately normal. Can you conclude that the mean volume...
Include null and alternate hypothesis, a p-value, and a conclusion PRIVATE about the null hypothesis A...
Include null and alternate hypothesis, a p-value, and a conclusion PRIVATE about the null hypothesis A student claimed that the average grade in the night sections of Statistics was higher than the day sections. She used a sample of 35 students from night sections and found they had a mean of 78 with a standard deviation of 8. A sample of 32 day students had a mean of 75 with a standard deviation of 6. Is the student's hypothesis supported?...
Compare and Contrast alternate hypothesis and null hypothesis. How do these concepts relate to each other?...
Compare and Contrast alternate hypothesis and null hypothesis. How do these concepts relate to each other? Provide an example of when you would use a one-tailed test. Finally, provide an example of when you would use a two-tailed test.
Define the null hypothesis, and the alternate hypothesis Define the acceptance region Define a one-sided alternate...
Define the null hypothesis, and the alternate hypothesis Define the acceptance region Define a one-sided alternate hypothesis and two-two sided alternate hypothesis Define the α error Define the β error Define a type I error and a type-II error. In terms of fixed significance testing, define the P-value.
Define the null hypothesis, and the alternate hypothesis Define the acceptance region Define a one-sided alternate...
Define the null hypothesis, and the alternate hypothesis Define the acceptance region Define a one-sided alternate hypothesis and two-two sided alternate hypothesis Define the α error Define the β error Define a type I error and a type-II error. In terms of fixed significance testing, define the P-value.
Include null and alternate hypothesis, a p-value, and a conclusion PRIVATE about the null hypothesis Nine...
Include null and alternate hypothesis, a p-value, and a conclusion PRIVATE about the null hypothesis Nine students took the SAT. After taking it, they then took a test preparation course and retook the SAT. Can you conclude that the course changes performance on the SAT? (use α = .1) Before 720 860 850 880 860 710 850 1200 950 After 740 860 840 920 890 720 840 1240 970
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT