Practice Math Statistics Problems and Master the Concepts

A. Look for the definitions of the following terms related to hypothesis testing.
1. Null Hypothesis
2. Level of Significance
3. Type I error

naivlingr 2020-12-28

Is statistical inference intuitive to babies? In other words, are babies able to generalize from sample to population? In this study,1 8-month-old infants watched someone draw a sample of five balls from an opaque box. Each sample consisted of four balls of one color (red or white) and one ball of the other color. After observing the sample, the side of the box was lifted so the infants could see all of the balls inside (the population). Some boxes had an “expected” population, with balls in the same color proportions as the sample, while other boxes had an “unexpected” population, with balls in the opposite color proportion from the sample. Babies looked at the unexpected populations for an average of 9.9 seconds ($sd = 4.5$ seconds) and the expected populations for an average of 7.5 seconds ($sd = 4.2$ seconds). The sample size in each group was 20, and you may assume the data in each group are reasonably normally distributed. Is this convincing evidence that babies look longer at the unexpected population, suggesting that they make inferences about the population from the sample? Let group 1 and group 2 be the time spent looking at the unexpected and expected populations, respectively. A) Calculate the relevant sample statistic. Enter the exact answer. Sample statistic: _

B) Calculate the t-statistic. Round your answer to two decimal places. t-statistic = _

C) Find the p-value. Round your answer to three decimal places. p-value =____

Chardonnay Felix 2020-12-28

The table shows the population of various cities, in thousands, and the average walking speed, in feet per second, of a person living in the city. $\begin{array}{cc} P o p u l a t i o n (t h o u s a n d s) & W a l k i n g S p e e d (f e e t p e r s e c o n d) \\ 5.5 & 0.6 \\ 14 & 1.0 \\ 71 & 1.6 \\ 138 & 1.9 \\ 342 & 2.2 \end{array}$

Khaleesi Herbert 2020-12-27

The scatter plot below shows the average cost of a designer jacket in a sample of years between 2000 and 2015. The least squares regression line modeling this data is given by $\hat{y} = - 4815 + 3.765 x .$ A scatterplot has a horizontal axis labeled Year from 2005 to 2015 in increments of 5 and a vertical axis labeled Price ($) from 2660 to 2780 in increments of 20. The following points are plotted: $(2003, 2736), (2004, 2715), (2007, 2675), (2009, 2719), (2013, 270)$ . All coordinates are approximate. Interpret the y-intercept of the least squares regression line. Is it feasible? Select the correct answer below: The y-intercept is −4815, which is not feasible because a product cannot have a negative cost. The y-intercept is 3.765, which is not feasible because an expensive product such as a designer jacket cannot have such a low cost. The y-intercept is −4815, which is feasible because it is the value from the regression equation. The y-intercept is 3.765 which is feasible because a product must have a positive cost.

CheemnCatelvew 2020-12-27

Consider the next 1000 98% Cis for mu that a statistical consultant will obtain for various clients. Suppose the data sets on which the intervals are based are selected independently of one another. How many of these 1000 intervals do you expect to capture the corresponding value of $μ ?$
What is the probability that between 970 and 990 of these intervals conta the corresponding value of Y =the number among the 1000 intervals that contain What kind of random variable is Y) (Use the normal approximation to the binomial distribution)

necessaryh 2020-12-25

True // False: comparing means. Determine if the following statements are true or false, and explain your reasoning for statements you identify as false.
(a) When comparing means of two samples where $n_{1} = 20$
and $n_{2} = 40$ ,
we can use the normal model for the difference in means since $n_{2} \geq 30.$
(b) As the degrees of freedom increases, the t-distribution approaches normality.
(c) We use a pooled standard error for calculating the standard error of the difference between means when sample sizes of groups are equal to each other.

UkusakazaL 2020-12-25

Suppose that $| G | = 24$ and that G is cyclic. If a8 e and a12 e, show that = G.

Sinead Mcgee 2020-12-25

The magazine Consumer Reports publishes information on automobile gas mileage and variables that affect gas mileage. In one issue, data on gas mileage (in miles per gallon) and engine displacement (in liters) were published for 121 vehicles. a) Obtain a scatterplot for the data. b) Decide whether finding a regression line for the data is reasonable. If so, then also do parts (c)-(f). c) Determine and interpret the regression equation for the data. d) Identify potential outliers and influential observations. e) In case a potential outlier is present, remove it and discuss the effect. f) In case a potential influential observation is present, remove it and discuss the effect.

Bergen 2020-12-25

Provide three examples of studies when we can use (a) the pooled, (b) non-pooled, and (3) paired inference to compare means of two populations.

chillywilly12a 2020-12-25

Explain what changes would be required so that you could analyze the hypothesis using a chi-square test. For instance, rather than looking at test scores as a range from 0 to 100, you could change the variable to low, medium, or high. What advantages and disadvantages do you see in using this approach? Which is the better option for this hypothesis, the parametric approach or nonparametric approach?

Reggie 2020-12-25

The International Business Society conducts a series of managerial surveys to detect challenges that international managers encounter and what strategies help them overcome those challenges. A previous study showed that employee retention is the most critical organizational challenge currently confronted by international managers. One strategy that may impact employee retention is a successful employee recognition program. The International Business Society randomly selected 423 small firms and 192 large firms. The study showed that 326 of the 423 small firms have employee retention programs compared to 167 of the 192 large organizations.
a) At the 0.01 level of significance, is there evidence of a significant difference between small firms and large firms concerning the proportion that has employee recognition program?
b) Find the p-value and interpret its meaning?
c) Construct and interpret a $99 %$ confidence interval estimate for the difference between small firms and large firms concerning the proportion of employee recognition program.

Suman Cole 2020-12-25

Show that the equation represents a sphere, and find its center and radius.
$x^{2} + y^{2} + z^{2} + 8 x - 6 y + 2 z + 17 = 0$

Amari Flowers 2020-12-25

What coordinate system is suggested if the integrand of a triple integral involves $x^{2} + y^{2} ?$

Emily-Jane Bray 2020-12-25

Which of the following are correct general statements about the Central Limit Theorem? Select all that apply.
1. It specifies the specific shape of the curve which approximates certain sampling distributions.
2. It’s name is often abbreviated by the three capital letters CLT
3. The word Central within its name, is meant to signify its role of central importance in the mathematics of probability and statistics.
4. The accuracy of the approximation it provides, improves when the trial success proportion p is closer to $50 %$ .
5. It specifies the specific mean of the curve which approximates certain sampling distributions.
6. The accuracy of the approximation it provides, improves as the sample size n increases.
7. It specifies the specific standard deviation of the curve which approximates certain sampling distributions.
8. It is a special example of the particular type of theorems in mathematics, which are called limit theorems.

Wierzycaz 2020-12-25

What is enterprise data modeling?

Braxton Pugh 2020-12-25

True or false to each of the statements in parts (a) and (b), and explain your reasoning. a. Two data sets that have identical frequency distributions have identical relative-frequency distributions. b. Two data sets that have identical relative-frequency distributions have identical frequency distributions. c. Use your answers to parts (a) and (b) to explain why relativefrequency distributions are better than frequency distributions for comparing two data sets.

vestirme4 2020-12-25

Which kind of descriptive statistics can be included to summarize the quantitative data? if the distribution is skewed

nicekikah 2020-12-24

In general, the t test for correlated groups is a more powerful test than the sign test. Is this statement true? Explain why? Can you think of situations in which the sign test might be more powerful than the t test for correlated groups (assume N is the same for both tests, etc.)?

FobelloE 2020-12-24

For the same data, null hypothesis, and level of significance, if the conclusion is to reject $H_{0}$ based on a two-tailed test, do you also reject Ho based on a one-tailed test? Explain.

York 2020-12-24

In there a relationship between confidence intervals and two-tailed hypothesis tests? The answer is yes. Let c be the level of confidence used to construct a confidence interval from sample data. Let * be the level of significance for a two-tailed hypothesis test. The following statement applies to hypothesis tests of the mean: For a two-tailed hypothesis test with level of significance a and null hypothesis $H_{0} : m u = k$ we reject Ho whenever k falls outside the $c = 1 — α$ confidence interval for mu based on the sample data. When A falls within the $c = 1 — α$ confidence interval. we do reject $H_{0}$ . For a one-tailed hypothesis test with level of significance Ho : mu = k and null hypothesiswe reject Ho whenever A falls outsidethe $c = 1 — 2 α$ confidence interval for p based on the sample data. When A falls within the $c = 1 — 2 α$ confidence interval, we do not reject $H_{0}$ . A corresponding relationship between confidence intervals and two-tailed hypothesis tests is also valid for other parameters, such as $p, μ_{1} — μ_{2},$ and $p_{1}, - p_{2}$ . (b) Consider the hypotheses $H_{0} : p_{1} — p_{2} = O$ and $H_{1} : p_{1} — p_{2} =$ Suppose a 98% confidence interval for $p_{1} — p_{2}$ contains only positive numbers. Should you reject the null hypothesis when alpha = 0.05? Why or why not?

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