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6.3. A survey was conducted at Malamulele Secondary School to establish how many of the 650 learners buy vetkoek and how many buy muffins in the morning. The following was found - 50 leaners bought nothing - 400 learners bought vetkoek 6.3.1. Represent the information on a Venn diagram. 6.3.2. How many learners bought both the vetkoek and the muffin? 6.3.3. If a learner is chosen at random, calculate the probability of a learner that does not buy muffins as a percentage.

Exercise 1: One hundred subjects in a psychological study had a mean score of \( M=35 \) on a test instrument designed to measure anger. The standard deviation of the \( n=100 \) test scores was \( \sigma=10 \). Find: a. A \( 99 \% \) confidence interval for the mean of the population the sample was selected. b. A \( 95 \% \) confidence interval for the mean of the population the sample was selected. c. A \( 96 \% \) confidence interval for the mean of the population the sample was selected. d. A \( 80 \% \) confidence interval for the mean of the population the sample was selected

Exercise 1: One hundred subjects in a psychological study had a mean score of \( M=35 \) on a test instrument designed to measure anger. The standard deviation of the \( =100 \) test scores was \( \sigma=10 \). Find: a. A \( 99 \% \) confidence interval for the mean of the population the sample was selected. b. A \( 95 \% \) confidence interval for the mean of the population the sample was selected. c. A \( 96 \% \) confidence interval for the mean of the population the sample was selected. d. A \( 80 \% \) confidence interval for the mean of the population the sample was selected

Una encuesta respondida por 1.000 estudiantes de un colegio A concluye que 726 no tie hábito de lectura. En otro colegio B se realizó la misma encuesta a 760 estudiantes, c cluyéndose que 240 de ellos tienen hábito de lectura. Calcule un intervalo de confianza \( 95 \% \) para la diferencia entre la proporción de estudiantes que tienen hábito de lectura en las dos encuestas. ¿Hay una diferencia significativa?

Exercise I: One hundred subjects in a psychological study had a mean score of \( M=35 \) on a test instrument designed to measure anger. The standard deviation of the \( n=100 \) test scores was \( \sigma=10 \). Find: a. A \( 99 \% \) confidence interval for the mean of the population the sample was selected. b. A \( 95 \% \) confidence interval for the mean of the population the sample was selected.

You wish to test the following claim ( \( H_{a} \) ) at a significance level of \( \alpha=0.002 \). \[ \begin{array}{l}H_{0}: \mu_{1}=\mu_{2} \\ H_{a}: \mu_{1}>\mu_{2}\end{array} \] You believe both populations are normally distributed, but you do not know the standard deviations for either. However, you also have no reason to believe the variances of the two populations are not equal. You obtain a sample of size \( n_{1}=20 \) with a mean of \( M_{1}=51.3 \) and a standard deviation of \( S D_{1}=13.2 \) from the first population. You obtain a sample of size \( n_{2}=23 \) with a mean of \( M_{2}=38.8 \) and a standard deviation of \( S D_{2}=8.7 \) from the second population.

Find the P-value: Type your answer as a decimial rounded to three decimal places. Do not type a percentage or a percent sign. P.value \( =.055 \) Using an \( \alpha \) level of \( 5 \% \), you should OReject \( H_{0} \) and Accept \( H_{A} \) Accept \( H_{0} \) OFail to Reject \( H_{0} \)

Will the sampling distribution of \( \bar{x} \) always be approximately normally distributed? Explain. Choose the correct answer below. A. Yes, because the Central Limit Theorem states that the sampling distribution of \( \bar{x} \) is always approximately normally distributed. B. No, because the Central Limit Theorem only states that the sampling distribution of \( \bar{x} \) is approximately normally distributed if the sample size is large enough. C. No, because the Central Limit Theorem states that the sampling distribution of \( \bar{x} \) is approximately normally distributed only if the population being sampled is normally distributed. D. No, because the Central Limit Theorem only states that the sampling distribution of \( \bar{x} \) is approximately normally distributed if the sample size is more than \( 5 \% \) of the population.

Exam Grades \( A \) statistics professor is used to having a variance in his class grades of no more than 100 . He feels that his current group of students is different, and so he examines a random sample of midterm grades (listed below). At \( \alpha=0.01 \), can it be concluded that the variance in grades exceeds 100 ? Assume the variable is normally distribujed. \( \begin{array}{ccccccc}68.7 & 49.1 & 75.8 & 52.8 & 92.3 & 96.7 & 89.4 \\ 65.2 & 69.5 & 72.8 & 67.5\end{array} \) Send data to Excel.

A local TV station wished to determine if a higher proprotion of women watch the local new They conduct a survey of 200 women and 200 men. Of those surveyed, \( 59 \% \) of women and \( 51 \% \) of men say they watch the local news. Find the P-value: Type your answer as a decimial rounded to three decimal places. Do not type a percentage or a percent sign. P-value=