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## Question 1 of 7

Four medical drugs with the same active ingredient are compared in terms of side effects. 200 persons participate in a study where the side effects for the individual person is categorized as none / light / serious. The results of the investigation is shown in the table below:

Category A B C D Total
No side effects 5 3 10 2 20
Light side effects 32 32 21 40 125
Serious side effects 13 15 19 8 55
Sum 50 50 50 50 200

If the entire data material is used, a 95% confidence interval for the proportion of serious side effects becomes:

## Question 2 of 7

If you did the previous exercise, the following is a repetition:

Four medical drugs with the same active ingredient are compared in terms of side effects. 200 persons participate in a study where the side effects for the individual person is categorized as none / light / serious. The results of the investigation is shown in the table below:

Category A B C D Total
No side effects 5 3 10 2 20
Light side effects 32 32 21 40 125
Serious side effects 13 15 19 8 55
Sum 50 50 50 50 200

Apart from the overall test, an investigation is wanted to find out whether the proportion of serious side effects is different for drug D than for the others. Hence, the following hypothesis test is performed:

$\begin{array}{l} {H_0}:{p_D} = {p_{others}}\\ {H_1}:{p_D} \not= {p_{others}} \end{array}$

The test statistic and P-value for this hypothesis test are:

## Question 3 of 7

A company sells weather modification rockets aimed a triggering precipitations in clouds. In order to assess the efficiency of this process, measurements are carried out in two regions with similar climatological features over 100 different non-consecutive days.

The amount of rain on region 1 (without cloud insemination) and region 2 (with cloud insemination) were summarized by the proportion of rainy days $p$, the average rainfall amount for rainy days $m$ and the sample standard deviation of rainfall amount for rainy days $s$: $p_1=0.51$, $p_2=0.68$, $\bar{x}_1=5.97$mm, $\bar{x}_2=8.25$mm, $s_1=\sqrt{23}$mm, $s_2=\sqrt{21}$mm.

Which of the following statements about the process is mostly correct?

## Question 4 of 7

If you did the previous exercise, the following is a repetition:

A company sells weather modification rockets aimed a triggering precipitations in clouds. In order to assess the efficiency of this process, measurements are carried out in two regions with similar climatological features over 100 different non-consecutive days.

The amount of rain on region 1 (without cloud insemination) and region 2 (with cloud insemination) were summarized by the proportion of rainy days $p$, the average rainfall amount for rainy days $m$ and the sample standard deviation of rainfall amount for rainy days $s$: $p_1=0.51$, $p_2=0.68$, $\bar{x}_1=5.97$mm, $\bar{x}_2=8.25$mm, $s_1=\sqrt{23}$mm, $s_2=\sqrt{21}$mm.

Which of the following statements is mostly correct?

## Question 5 of 7

In relation to medicine development, a number of candidates are designed on molecular level. For 832 drugs, the following correlation coefficients between the three properties, MW (molecular weigh), SURF (molecular surface area) and VOL (molecular volume) are achieved:

cors SURF VOL MW
SURF 1 0.995 0.949
VOL 0.995 1 0.952
MW 0.949 0.952 1

If we fit the following regression model to the data:

$$\mbox{MW}_i=\alpha + \beta\cdot \mbox{SURF}_i + \varepsilon_i$$, how much of the variation in $\mbox{MW}_i$ will be explained?

## Question 6 of 7

If you did the previous exercise, the following is a repetition:

In relation to medicine development, a number of candidates are designed on molecular level. For 832 drugs, the following correlation coefficients between the three properties, MW (molecular weigh), SURF (molecular surface area) and VOL (molecular volume) are achieved:

cors SURF VOL MW
SURF 1 0.995 0.949
VOL 0.995 1 0.952
MW 0.949 0.952 1

Assume that we have fitted the following regression model to the data:

$$\mbox{VOL}_i=\alpha + \beta\cdot \mbox{SURF}_i + \varepsilon_i$$ If molecule A has a surface area (SURF) equal to 200 areal units larger than molecule B (that is\ $\mbox{SURF}_A=\mbox{SURF}_B + 200$), the expected volume of molecule A is given with:

## Question 7 of 7

In a study of 712 medicine candidates, the mean molecular weight was found to be 437 with standard deviation of 117.

Within what limits are 95% of this type of medicine expected to lie within?