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In Exercise 4.2.18 we found a confidence interval for the variance σ2 using  Exercise 4.2.18 Let  be a random sample from N(μ, σ2), where both param  (a) Show that this second probability statement can be written as (b) If n = 9 and s2 = 7.93, find a 95% confidence interval for σ2. (c) If μ is known, […]

Let p equal the proportion of drivers who use a seat belt in a country that does not have a mandatory seat belt law. It was claimed that p = 0.14. An advertising campaign was conducted to increase this proportion. Two months after the campaign, y = 104 out of a random sample of n

Among the data collected for the World Health Organization air quality monitoring project is a measure of suspended particles in μg/m3. Let X and Y equal the concentration of suspended particles in μg/m3 in the city center (commercial district) for Melbourne and Houston, respectively. Using n = 13 observations of X and m = 16 observations

A number is to be selected from the interval by a random hypothesis (concerning the multinomial pdf with k = 4) is to be tested at the 5% level of significance by a chi-square test. If the observed frequencies of the sets Ai, i = 1, 2, 3, 4, are respectively, 30, 30, 10, 10,

Consider Example 4.7.2. Suppose the observed frequencies of are 20, 30, 92, and 105, respectively. Modify the R code given in the example to calculate the test for these new frequencies. Report the p-value. Example 4.7.2

In Exercise 4.2.27, in finding a confidence interval for the ratio of the variances of two normal distributions, we used a statistic  which has an Fdistribution when those two variances are equal. If we denote that statistic by F,  Exercise 4.2.27 Let  be two independent random samples from the respective normal distributions  where the four parameters are unknown.

Define the setsA certain hypothesis assigns probabilities pi0 to these sets Ai in accordance with This hypothesis (concerning the multinomial pdf with k = 8) is to be tested, at the 5% level of significance, by a chi-square test. If the observed frequencies of the sets Ai, i = 1, 2,…, 8, are, respectively, 60,

A die was cast n = 120 independent times and the following data resulted: If we use a chi-square test, for what values of b would the hypothesis that the die is unbiased be rejected at the 0.025 significance level?

Let the result of a random experiment be classified as one of the mutually exclusive and exhaustive ways and also as one of the mutually exhaustive ways . Say that 180 independent trials of the experiment result in the following frequencies: where k is one of the integers 0, 1, 2, 3, 4, 5. What

Kloke and McKean (2014) present a data set concerning crime and alcoholism. The data they discuss is in Table 4.7.1. It contains the frequencies of criminals who committed certain crimes and whether or not they are alcoholics. The data are also in the file crimealk.rda. (a) Using code similar to that given in Exercise 4.7.6,