Practice Math Statistics Problems and Master the Concepts

A Harris Interactive survey for InterContinental Hotels & Resorts asked respondents, “When traveling internationally, do you generally venture out on your own to experience culture, or stick with your tour group and itineraries?” The survey found that 23% of the respondents stick with their tour group (USA Today, January 21, 2004).

a. In a sample of six international travelers, what is the probability that two will stick with their tour group?
b. In a sample of six international travelers, what is the probability that at least two will stick with their tour group?
c. In a sample of 10 international travelers, what is the probability that none will stick with the tour group?

Adolfo Hebert 2022-03-21

Let $X_{1}, \dots X_{n}$ be iid $N (θ, 1)$ . A $95 %$ confidence interval for $θ$ is $\overset{―}{X} \pm \frac{1.96}{\sqrt{n}}$ . Let p denote the probability that an additional independent observation, $X_{n + 1}$ , will fall in this interval. Is p greater than, less than, equal to $0.95$ ? Prove your answer.

svezic0rn 2022-03-21

Let $X_{1}, \dots, X_{n}$ be a random sample from $f (x ∣ θ) = θ x^{θ - 1}$ for $0 < x < 1$ . Find a confidence interval for $θ$ using as pivotal quantity a function of the maximum likelihood estimator for $θ$ .

Jazmyn Holden 2022-03-21

Let $\overset{―}{X}$ be the mean of a random sample of size n from $N (μ, 9)$ . Find n so that $P (\overset{―}{X} - 1 < μ < \overset{―}{X} + 1) = .9$
This problem is given at the end of a chapter in my statistics textbook concerning confidence intervals for means.

Litzy Wallace 2022-03-21

Let K be the number of heads in 200 flips of a coin. The null hypothesis H is that the coin is fair. Devise significance tests with the folowng properties.
Note: Your answers below must be integers
a) The signficance level is $α$ =0.08 and the rejection set R has the form ${| K - E [K] | > c} .$
Use the Central Limit theorem to find the accsptane ce set A.
$A = {\dots, \dots, \dots}$
b) Now tho significance level is $α$ = 0.016 and the rejection set R has the form ${K > c^{1}}$
Again, use tho Central Limit Theorem to find tho accaptance set A.
$A = {\dots, \dots, \dots}$

Juliet Jackson 2022-03-19

Choose the appropriate test for the following situation: You wish to test whether an association exists between the type of vehicle purchased and how many children the buyer has.
a) Chi-square test
b) One-sample t-test
c) Two-sample t-test
d) ANOVA

fun9vk 2022-03-19

Can a 2 paired sample sets of size 15 (30 readings in total) be assumed to have normal distribution when finding confidence intervals?
I've seen that for large sample sizes (about 30 or more) the distribution tends to a normal distribution, but what if I have 2 sets of 15 which are paired? Would that count as a normal distribution, or would I need to use a t-distribution to approximate confidence intervals for the difference between their means?

Carmen Bowers 2022-03-19

Calculate the test statistic $χ^{2}$ and state your decision regarding the null hypothesis. 23.
It has been rumored that the color distribution of M&M's is 30% brown, 20% yellow, 20% red, 10% orange, 10% blue, and 10% green. You suspect this rumor is incorrect and decide to count how many of each color are contained in a randomly chosen bag in order to perform a Chi-Square goodness-of-fit test at a 5% significance level.
$\begin{array}{cc} Color \\ Brown & Yellow & Red & Orange & Blue & Green & Total \\ Observed & 27 & 16 & 21 & 12 & 9 & 15 & 100 \end{array}$
Provided the assumptions of the test are satisfied, calculate the test statistic $χ^{2}$ :
a. 4.15, Reject $H_{0}$
b. 4.15, Fail to Reject $H_{0}$
c. 16.83, Reject $H_{0}$
d. 16.83, Fail to Reject $H_{0}$

Jaylan Chung 2022-03-19

Based on a survey of a random sample of 900 adults in the United States, a journalist reports that A random sample of 100 movie goers was asked to state his or her gender and favorite soft drink available at the local movie theater. The results appear in the table below. Is there a relationship between gender and soft drink preference?
$\begin{array}{cccc} Coke & Diet Coke & Sprite \\ Male & 23 & 11 & 12 \\ Female & 16 & 28 & 10 \end{array}$
To analyze the results, which of the following tests is most appropriate?
A)Chi-square test of independence
B)Chi-square test of homogeneity
C)Two sample t-test
D)Matched pair t-test
E)Chi-square goodness of fit

A strawberry jam company regularly receives large shipments of strawberries. For each shipment that is received, a supervisor takes a random sample of 500 strawberries to see what percent of the sample is bruised and performs a significance test. If the sample shows convincing evidence that more than 10%, percent of the entire shipment of strawberries is bruised, then they will request a new shipment of strawberries.

Let p represent the proportion of the strawberries in a shipment that are bruised.

adoliremdhp 2022-03-18

Are they both used to calculate the confidence interval at $95 %$ for a population proportion?
Here are two questions from my book.
In a survey in a large city, 170 households out of 250 owned a pet. Find the $95 %$ confidence interval for the proportion of households in the city who own a pet.
From a random sample, 136 out of 400 people experience discomfort after receiving a vaccine. Construct a $95 %$ confidence interval for the population proportion who might experience discomfort.
For each question do I use: $\hat{p} \pm \frac{1}{\sqrt{n}}$ or $\hat{p} \pm \sqrt{\frac{p (1 - p)}{n}}$ ?

nevinijifg8 2022-03-18

A study was recently conducted in which people were asked to indicate which news medium was their preferred choice for national news. The following data were observed:
$\begin{array}{cc} radio & television & newspaper \\ under 21 & 30 & 50 & 5 \\ 21-40 & 20 & 25 & 30 \\ 41 and over & 30 & 30 & 50 \end{array}$
Given this data, if we wish to test whether the preferred news source is independent of age, for an alpha = .05 level, the critical value from the chi-square table is based on 8 degrees of freedom.
Seleccione una:
a. Verdadero
b. Falso

Carmen Bowers 2022-03-18

A survey was conducted to investigate the relationship between gender (male and females) and sector of employment (private, government and academia). Using the information provided, does a relationship exist between gender and employment sector at the 5% significance level? If the Chi-square test statistics = 0.529, what conclusion can be made?
A. Since Chi-square test statistics > Chi-square critical value, do not reject $H_{0}$
B. Since Chi-square test statistics < Chi-square critical value, do not reject $H_{0}$
C. Since Chi-square test statistics < Chi-square critical value, Reject $H_{0}$
D. Since Chi-square test statistics > Chi-square critical value, Reject $H_{0}$

Jeffrey Ali 2022-03-18

A study of the population of NUIG students showed that out of a sample of 155 students surveyed, 45 said they regularly cooked their own food during term time.Carry out a hypothesis test to determine if this gives evidence that more than 25% of the population of NUIG students regularly cooked their own food during term time, i.e test the hypotheses for true population proportion, $H_{0}$ : p= 0.25 versus $H_{a}$ : p > 0.25, at significance level $α$ = 0.05
Complete the test by filling in the blanks in the following:
An estimate of the population proportion is .The standard error is . (3 dec places)The distribution is (examples: normal / t12 / chisquare4 / F5,6).The test statistic has value TS=. (2 dec places)Testing at significance level α = 0.05, the rejection region is: greater than (2 dec places).There (is / is no) evidence to suggest that the true proportion of the population of all NUIG students who regularly cooked their own food during term time, p, is greater than 0.25.

evighetl2b 2022-03-18

A study was conducted to investigate whether there are regional differences in peanut butter preference in the United States. The country was divided into 7 geographic regions, and in each region a random sample of peanut butter eaters were asked whether they preferred creamy or crunchy peanut butter. The responses were summarized in a 7-by-2 table of counts for each combination of geographic region and creamy or crunchy peanut butter preference.
A. A two-sample z-test for a difference between proportions
B. A chi-square test of homogeneity
C. A chi-square test of independence
D. A chi-square goodness-of-fit test

Lisa Vaughan 2022-03-18

A study compared men who viewed high levels of television violence as children with those who did not in order to study the differences with regard to physical abuse of their partners as adults. Test to see if watching TV violence has something to do with physical abuse of their partners as adults.
$\begin{array}{ccc} Category & High TV Violence & Low TV Violence \\ Yes, Physical Abuse & 15 & 29 \\ Yes, Physical Abuse & 17 & 94 \end{array}$
What is the name of this hypothesis test?
1. One Sample z Test
2. Chi-Square Test for Independence
3. Two Proportion z Test
4. Chi-Square Goodness of Fit Test
5. Linear Regression t Test
6. Two Independent Samples t Test
7. Paired Samplest t Test
8. One Sample t Test
9. Two Proportion z Test
10. ANOVA F Test
11. One Proportion z Test
There are two variables of this study. What are they?
1. Yes Physical Abuse and No Physical Abuse
2. Violence and Abuse
3. High TV Violence and Low TV Violence

meiprate81w 2022-03-18

A state is considering legislation to establisha law to help homeless individuals. A sample of 309 individuals regarding their opinions on the potential new law. Is there a relationship between sex and support for this law? Calculate the expected frequencies and compute a chi-square test for a statistically significant relationship between sex and support for the new law. Be sure to round to the second decimal.
$\begin{matrix} Sex \\ Support & \begin{array}{ccc} Male & Female \\ For & 98 & 101 \\ Against & 29 & 81 \end{array} \end{matrix}$

Thalia Ortiz 2022-03-18

A sample of 25 circuit boards yields 2 defective boards after testing. What would be confidence interval for the true proportion of circuit boards in the lot from which the sample was drawn? Use the Clopper-Pearson Interval and also a normal approximation interval. In yur own words which do feel is better to use and why?

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