### Comparing Frost and Arcane Spell EffectivenessA mage is trying to decide which kind of spell to specialize in for her upcoming adventure. She reviews a survey conducted by her fellow mages to assess the damage per second against monsters for Frost spells versus Arcane spells. The data collected is as follows:- **Frost Spells** - Sample size ($n_1$): 250 - Mean damage ($\bar{x}$): 3.61 - Standard deviation ($s_1$): 1.3- **Arcane Spells** - Sample size ($n_2$): 238 - Mean damage ($\bar{y}$): 3.26 - Standard deviation ($s_2$): 1.1**Hypothesis Test**Using a significance level ($\alpha$) of 0.05, the question posed is: Is there sufficient statistical evidence to conclude that Frost mages deal more damage per second than Arcane mages? This analysis will typically involve conducting a hypothesis test to compare means, such as a t-test for independent samples.

Name: ### Comparing Frost and Arcane Spell EffectivenessA mage is trying to
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Description: ### Comparing Frost and Arcane Spell EffectivenessA mage is trying to decide which kind of spell to specialize in for her upcoming adventure. She reviews a survey conducted by her fellow mages to assess the damage per second against monsters for Fro

The given data is : n1=250n2=238x=3.61y=3.26s1=1.3s2=1.1 Task is to compare the damage made by frost spell and arcane spell. The hypothesis are : Ho : μ1=μ2H1 : μ1>μ2 The sample is fairly large so standard normal distribution will be applied. The test statistics is therefore given as : z=x-ys21n1+s22n2~N(0,1) z=3.61-3.261.32250+1.12238=0.350.00676+0.00508=0.350.1088=3.2169The critical z-value at α=0.05 level of significance is 1.645 (one-tailed) Decision rule states, reject the null hypothesis when calculated test statistics is greater than the tabulated z-value. 3.2169 > 1.645 - Reject Ho Conclusion : Failed to reject the null hypothesis. Therefore there are sufficient evidence that frost mages do more damage per second than arcane mages.

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1. A mage is trying to decide which kind of spell to specialise in for her upcoming adventure. She looks at survey done by her fellow mages on the kind of damage per second that they're doing against monsters to compare Frost spells against Arcane spells, and gathers the following data: standand deviation Sample size n1 = 250 mean a = 3.61 Frost ypba$1 = 1.3 Arcane n2 = 238 j = 3.26 $2 = 1.1 Using a = .05, is there sufficient statistical evidence that frost mages do more damage per second than arcane mages?

1. A mage is trying to decide which kind of spell to specialise in for her upcoming adventure. She looks at survey done by her fellow mages on the kind of damage per second that they're doing against monsters to compare Frost spells against Arcane spells, and gathers the following data: standand deviation Sample size n1 = 250 mean a = 3.61 Frost ypba$1 = 1.3 Arcane n2 = 238 j = 3.26 $2 = 1.1 Using a = .05, is there sufficient statistical evidence that frost mages do more damage per second than arcane mages?

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Concept explainers

Contingency Table

A contingency table can be defined as the visual representation of the relationship between two or more categorical variables that can be evaluated and registered. It is a categorical version of the scatterplot, which is used to investigate the linear relationship between two variables. A contingency table is indeed a type of frequency distribution table that displays two variables at the same time.

Binomial Distribution

Binomial is an algebraic expression of the sum or the difference of two terms. Before knowing about binomial distribution, we must know about the binomial theorem.

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Question

### Comparing Frost and Arcane Spell Effectiveness

A mage is trying to decide which kind of spell to specialize in for her upcoming adventure. She reviews a survey conducted by her fellow mages to assess the damage per second against monsters for Frost spells versus Arcane spells. The data collected is as follows:

- **Frost Spells**
- Sample size ($n_1$): 250
- Mean damage ($\bar{x}$): 3.61
- Standard deviation ($s_1$): 1.3

- **Arcane Spells**
- Sample size ($n_2$): 238
- Mean damage ($\bar{y}$): 3.26
- Standard deviation ($s_2$): 1.1

**Hypothesis Test**

Using a significance level ($\alpha$) of 0.05, the question posed is: Is there sufficient statistical evidence to conclude that Frost mages deal more damage per second than Arcane mages? This analysis will typically involve conducting a hypothesis test to compare means, such as a t-test for independent samples.

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