Statistics for Data Science II End Term: 8 August 2021 (May 2021 term)

Shruti will read either one chapter of her Geography book or one chapter of her history book with equal probability. The number of misprints in a chapter of her Geography book is Poisson distributed with mean 2 and the number of misprints in a chapter of her history book is Poisson distributed with mean 5. What is the expected number of misprints that she will come across in a chapter? Enter your answer correct to one decimal place.

Based on the above data, answer the given subquestions.

Based on the above data, answer the given subquestions.

Find the method of moments estimate of θ from the samples 2, 5, 3, 6, 8, 4, 10, 7. Enter your answer correct to two decimal places.

Based on the above data, answer the given subquestions.

Determine the value of the test statistic when testing the independence of gender and voting. Enter your answer correct to two decimal places.

Based on the above data, answer the given subquestions.

A null hypothesis will be rejected when the value of the test statistic is large. The observed value of the test statistic is 1.3. Suppose that when the null hypothesis is true, the probability that the test statistic is at least 1.3 is 0.06.
Based on the above data, answer the given subquestions.

Will the null hypothesis be rejected at a significance level of 5%?

A null hypothesis will be rejected when the value of the test statistic is large. The observed value of the test statistic is 1.3. Suppose that when the null hypothesis is true, the probability that the test statistic is at least 1.3 is 0.06.
Based on the above data, answer the given subquestions.

Will the null hypothesis be rejected at a significance level of 10%?

An experiment was conducted to compare the alcohol content of cough syrup on two different production lines. It is suspected that variability of alcohol content is more on the production line 1. A sample of eight cough syrups from production line 1 has a sample standard deviation (s1) of 2.6, while a sample of ten cough syrups from production line 2 has a sample standard deviation (s2) of 2.2.
Based on the above data, answer the given subquestions.

State the null and alternative hypothesis.

An experiment was conducted to compare the alcohol content of cough syrup on two different production lines. It is suspected that variability of alcohol content is more on the production line 1. A sample of eight cough syrups from production line 1 has a sample standard deviation (s1) of 2.6, while a sample of ten cough syrups from production line 2 has a sample standard deviation (s2) of 2.2.
Based on the above data, answer the given subquestions.

Find the P-value of the test. Enter your answer correct to two decimal places.
(Use: FF(7,9)(1.396) = 0.686)

From previous data, we know that the annual rainfall, X in a particular region is normally distributed with E(X) = 998 mm. In recent years, due to various climate changes, it is hypothesized that in fact, the annual rainfall has decreased. Let us assume that the rainfall (in mm) registered in the past 8 years are as follows:
650, 802, 1198, 780, 850, 1150, 1200, 690.
Based on the above data, answer the given subquestions.

Identify the null and alternative hypotheses:

From previous data, we know that the annual rainfall, X in a particular region is normally distributed with E(X) = 998 mm. In recent years, due to various climate changes, it is hypothesized that in fact, the annual rainfall has decreased. Let us assume that the rainfall (in mm) registered in the past 8 years are as follows:
650, 802, 1198, 780, 850, 1150, 1200, 690.
Based on the above data, answer the given subquestions.

An editor of a newspaper wants to conduct a survey in order to estimate the proportion (p) of voters in the city. She uses a Beta(a, b) prior distribution for p. Data from other similar cities suggests an expected value of 0.6 and standard deviation of 0.2 for the proportion of voters. Based on the above data, answer the given subquestions.

Find the value of a and b.

An editor of a newspaper wants to conduct a survey in order to estimate the proportion (p) of voters in the city. She uses a Beta(a, b) prior distribution for p. Data from other similar cities suggests an expected value of 0.6 and standard deviation of 0.2 for the proportion of voters. Based on the above data, answer the given subquestions.

Find the posterior mean if out of a sample of 100 people she surveyed, 30 are voters. Enter the answer correct to two decimal places.

Based on the above data, answer the given subquestions.

What is the ML estimate of p. Enter your answer correct to two decimal places.

Based on the above data, answer the given subquestions.

Based on the above data, answer the given subquestions.

NOTE: Enter your answer to the nearest integer.