Concept explainers
Recall the data in Question 8.2.9 giving the sizes of ten gorilla groups studied in the Congo. Is it believable that the true median size,
Probability Density
Binomial with
0 | 0.000977 |
1 | 0.009766 |
2 | 0.043945 |
3 | 0.117188 |
4 | 0.205078 |
5 | 0.246094 |
6 | 0.205078 |
7 | 0.117188 |
8 | 0.043945 |
9 | 0.009766 |
10 | 0.000977 |
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Chapter 14 Solutions
EBK AN INTRODUCTION TO MATHEMATICAL STA
- For each of the following assertions, state whether it is a legitimate statistical hypothesis and why: H: σ > 100 H: x ̃= 45 H: s ≤ 0.20 H: σ1/σ2 < 1 H: λ ≤ 0.01, where λ is the parameter of an exponential distribution used to model component lifetimearrow_forward9.1) Suppose X1, X2, and X3, denotes a random sample from the exponential distribution with density function shown in the image. a) Which of the above estimators are unbiased for θ? b) Among the unbiased estimators of θ, which has the smallest variance?arrow_forwardQUESTION 11 An educator estimates that the dropout rate for seniors at high schools in Colorado is 15%. Last year in a random sample of 300 Colorado seniors, 34 withdrew from school. At α = 0.10 level of significance, is there enough evidence to reject the educator’s claim? Yes, because the p-value is 0.075 Yes, because the z-statistic is 1.6 No, because the p-value is 0.038 Yes, because the p-value is larger than 0.15arrow_forward
- answer b The following table shows the number of shirts by sizes that are manufactured in a factory on aparticular week:Extra Small Small Medium Large Extra Large390 470 520 680 440a) It was discovered that the sizing of some shirts was labelled incorrectly.(i) Give two reasons why it would be necessary to examine a sample of the shirts producedrather than examine the entire weekly production. (ii) State two differences between a cluster sample and a stratified random sample in thissituation. (iii) Using the stratified random sampling technique, calculate the number of medium shirtsthat will be selected if we require a sample of 375 shirts. (iv)State one advantage of using stratified random method for collecting this sample. b) Determine the level of measurement that describes the following (i) The size of the shirt that a customer purchase(ii) The total amount paid by the customer(iii) The address of the factory that manufactures the shirtsarrow_forwardIn my regression output using Hayes Model 1 I have the following results. Would it be safe to say that the following assumption is correct? 95% CI is [.036, .196] not statistically significant, But given that (p = .176) is greater than p=.005, we reject the null hypothesis. (b3) of .080, t = 1.36, p = .176, 95% CI [.036, .196].arrow_forwardQuestion 13: You wish to test the following claim (HaHa) at a significance level of α=0.005α=0.005. Ho:p=0.11Ho:p=0.11 Ha:p<0.11Ha:p<0.11You obtain a sample of size n=572n=572 in which there are 41 successful observations. For this test, you should NOT use the continuity correction, and you should use the normal distribution as an approximation for the binomial distribution.What is the critical value for this test? (Report answer accurate to three decimal places.)critical value = What is the test statistic for this sample? (Report answer accurate to three decimal places.)test statistic = The test statistic is... in the critical region not in the critical region This test statistic leads to a decision to... reject the null accept the null fail to reject the null As such, the final conclusion is that... There is sufficient evidence to warrant rejection of the claim that the population proportion is less than 0.11. There is not sufficient evidence to warrant…arrow_forward
- With the dataset from the naive Bayes question, use m-estimation (Laplacian smoothing) with m = 5 and prior estimate p(Rest=Yes|Healthy=Yes) = 1/2 to compute the following conditional probability: P(Rest = Yes|Healthy = Yes).arrow_forwardQ1. An anthropologist wants to collect data to determine whether the two different cultural groups that occupy an isolated Pacific Island grow to be different heights. The results of his samples of the heights of adult females are as follows Do these samples constitute enough evidence to reject the null hypothesis that the heights of the two groups the same? Set alpha to .05.arrow_forwardA researcher conducts a hypothesis test using a sample of n = 20 with M = 34 and s 2 = 36 from an unknown population. What is the df value for the t statistic?arrow_forward
- A researcher conducts a hypothesis test using a sample of n=20 with M =34 and s^2=36 from an unknown population.What is the df value for the t statistic?arrow_forwardAn atom in the ground state of a quantum harmonic oscillator has a wavefunction ψ(x) that gives rise to a probability distribution P(X)=|ψ(x)|^2 for the position of the particle X. For a specific harmonic oscillator potential, the wavefunction is given by: ψ(x)=(1/4*(2π)^1/4)e^(−x^2−4x+4/1024) By calculating |ψ(x)|^2 and rearranging the exponent, convince yourself that P(X) can be written as a properly normalised Gaussian distribution. (a) Find the mean μ of P(X) (b) Find the standard deviation σ of P(X) (c) Find the value of c such that P(X>c)=4P(X≤c)arrow_forwardIf X1 and X2 constitute a random sample of size n = 2from an exponential population, find the efficiency of 2Y1relative to X, where Y1 is the first order statistic and 2Y1and X are both unbiased estimators of the parameterarrow_forward
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