Hypothesis: Sales - training - calls

Hypothesis Testing: Mean Sales, Proportion of Online Training, Mean Calls, and Mean Time per Call

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Hypothesis Test 1: Mean Sales

1.Hypothesis Test 1

Step-1
The parameter of this hypothesis test 1 is mean sales per week.
Step- 2
    Null hypothesis (H0): The mean sales per week is not exceed 42.5 per salesperson.
            i.e. µ = 42.5
    Alternative hypothesis (H1): The mean sales per week is exceed 42.5 per salesperson.
            i.e. µ 42.5
Step- 3
    Test statistic (t) =
    Where
        n = total number of sample observation
        = Sample mean
        = Population mean
        s = sample standard deviation
Step- 4
    Alpha level = 0.05 (at 5%)
Step- 5
    Test statistic (t) = 1.5
Step – 6
    P- Value = 0.07
Step- 7
    The hypothesis test 1 shows that the P- value is larger than the alpha value. Thus this null hypothesis may not be rejected. Hence it can be concluded at 5% significance level that the mean sales per week is not exceed 42.5 per salesperson.
Step – 8
?The sample size should be more than 30.
?The P – Value should be more than alpha value.
?The sample observations should be normal.
Confidence Interval at 99%
    The 99% confidence interval for the mean sales per week is as below
            )
                 = 43.63)
                 = (41.71, 45.55)
The confidence interval is a type of interval which shows a range of values and this can be calculated from the sample observations. Moreover a confidence interval is an interval where the investigator is confident some percent that the parameter or subject of the test lie within this confidence range. In this case the 99% confidence interval for the mean sales per week shows that the mean sales lies between 41.71 and 45.55. Thus the investigator or researcher is 99% confident that the mean sales always lies between 41.71 and 45.55. Moreover the investigator is 1% not confident that this mean sale lie within this interval.
2.Hypothesis Test 2
Step-1
The parameter of this hypothesis test 2 is proportion of receiving online training.
Step- 2
    Null hypothesis (H0): The proportion of receiving online training is not less than 0.55
            i.e. P0 0.55
Alternative hypothesis (H1): The proportion of receiving online training is less than    0.55
            i.e. P0 0.55
Step- 3
    Test statistic (t) =
    Where
        n = total number of sample observation.
        P1=
           = Sample proportion
        P0 = Population proportion

Step- 4
    Alpha level = 0.05 (at 5%)
Step- 5
    Test statistic (t) = -2.41
Step – 6
    P- Value = 0.009
Step- 7
    The hypothesis test 2 shows that the P- value is lesser than the alpha value. Thus this null hypothesis may be rejected. Hence it can be concluded at 5% significance level that the proportion of receiving online training is less than 0.55 that is 55%.
Step – 8
?The sample size should be more than 30.
?The P – Value should be less than alpha value.
?The sample observations should be normal.
Confidence Interval at 99%
The 99% confidence interval for the proportion of receiving online training is as below
        P12.58*
Where
        P1=
                    =
                    = 0.43
                           0.432.58*
                          = (0.30, 0.56)
The confidence interval is a type of interval which shows a range of values and this can be calculated from the sample observations. Moreover a confidence interval is an interval where the investigator is confident some percent that the parameter or subject of the test lie within this confidence range. In this case the 99% confidence interval for the proportion of receiving online training is lies between 0.30 (30%) and 0.56 (56%). Thus the investigator or researcher is 99% confident that the proportion of receiving online training always lies between 30% and 56%. Moreover the investigator is 1% not confident that this proportion of receiving online training lies within this range or interval.
3.Hypothesis Test 3
    Step-1
The parameter of this hypothesis 3 test is mean calls among those with no training.
            Step- 2
    Null hypothesis (H0): The mean calls among those with no training is not at least 145.
            i.e. µ 145
Alternative hypothesis (H1): The mean calls among those with no training is at least 145.
            i.e. µ 145
Step- 3
    Test statistic (t) =
    Where
        n = total number of sample observation
        = Sample mean
        = Population mean
        s = sample standard deviation
Step- 4
    Alpha level = 0.05 (at 5%)
Step- 5
    Test statistic (t) = 8
Step – 6
    P- Value = 0.000
Step- 7
    The hypothesis test 3 shows that the P- value is lesser than the alpha value. Thus this null hypothesis may be rejected. That is significant. Hence it can be concluded at 5% significance level that the mean calls among those with no training is at least 145.
Step – 8
The sample size should be more than 30.
The P – Value should be less than alpha value.
The sample observations should be normal.
Confidence Interval at 99%
    The 99% confidence interval for the mean sales per week is as below
            )
                 = 160.33)
                 = (155.36, 165.30)
The confidence interval is a type of interval which shows a range of values and this can be calculated from the sample observations. Moreover a confidence interval is an interval where the investigator is confident some percent that the parameter or subject of the test lie within this confidence range. In this case the 99% confidence interval for the mean calls among those with no training shows that the mean calls with no training lies between 155.36 and 165.30. Thus the investigator or researcher is 99% confident that the mean calls among those with no training always lies between 155.36 and 165.30. Moreover the investigator is 1% not confident that this mean calls among those with no training lie within this interval or range.
4.Hypothesis Test 4
    Step-1
The parameter of this hypothesis test 4 is mean time per call.
             Step- 2
    Null hypothesis (H0): The mean time per call is not 14.7 minutes.
            i.e. µ 14.7
Alternative hypothesis (H1): The mean time per call is 14.7 minutes.
            i.e. µ = 14.7
            Step- 3
    Test statistic (t) =
    Where
        n = total number of sample observation
        = Sample mean
        = Population mean
        s = sample standard deviation
            Step- 4
    Alpha level = 0.05 (at 5%)
            Step- 5
    Test statistic (t) = 1.1
            Step – 6
     P- Value = 0.14
           Step- 7
    The hypothesis test 4 shows that the P- value is larger than the alpha value. Thus this null hypothesis may not be rejected. That is not significant. Hence it can be concluded at 5% significance level that the mean time per call is not 14.7 minutes.
          Step – 8
The sample size should be more than 30.
The P – Value should be more than the alpha value.
The sample observations should be normal.
Confidence Interval at 99%
    The 99% confidence interval for the mean sales per week is as below
            )
                 = 14.947)
                 = (14.35, 15.54)
The confidence interval is a type of interval which shows a range of values and this can be calculated from the sample observations. Moreover a confidence interval is an interval where the investigator is confident some percent that the parameter or subject of the test lie within this confidence range. In this case the 99% confidence interval for the mean time per call show’s that the parameter lies 14.35 and 15.54. Thus the investigator or researcher is 99% confident that the mean time per calls always lies between 14.35 and 15.54. Moreover the investigator is 1% not sure or confident that this mean time calls lie within this interval.