# Statistics and Probability Questions 2022

This assignment involves performing hypothesis tests on given data sets and calculating sample frequency mean and standard deviation for grouped data.

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## Statistics and Probability Questions 2022

This assignment involves performing hypothesis tests on given data sets and calculating sample frequency mean and standard deviation for grouped data.

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Running head: Statistics and probability 1
Statistics and Probability
Course code
Student name
Tutor
Statistics and Probability 2
QUESTION 1
1. Sample frequency mean and standard deviation
Mean 323.33
Std deviation 14.696
Table 1
2. Median, first and third quartile
Median 324
1st
Quartile 313.5
3rd
Quartile 334.5
Table 2
3. Since the mean and the median are almost equal, it can be concluded that the data is
approximately normally distributed.
4. Frequency polygon, histogram and cumulative frequency polygon
Frequency polygon
303 309 315 321 327 333 339 345
0
10
20
30
40
50
60
70
80
90
Frequency polygon
Frequency
Figure 1
Statistics and Probability 3
Histogram
303 309 315 321 327 333 339 345
0
10
20
30
40
50
60
70
80
90
Histogram
Frequency
Figure 2
Cumulative frequency polygon
303 309 315 321 327 333 339 345
0
50
100
150
200
250
300
cumulative frequency polygon
Figure 3
QUESTION 2
1.
Statistics and Probability 4
Mean = 200.24
Standard deviation = 3.75
X = 200
Z= x μ
σ
Z=200.24200
3.75 =0.064
P value corresponding to a Z-value of 0.064 for a two-tailed test at 0.05 level of significance is
0.94897
2. Hypothesis
H0: μ = 200
H1: μ ≠ 200
Alpha = 0.05
3. The structure of the test becomes a two-tailed test since the mean can either be greater or less
than 200 grams.
4. Since the p-value (0.95) is greater than the level of significance, the null hypothesis is not
rejected. It is concluded that the mean weight of the packets is 200 grams.
5.
Mean = 199.16
Standard deviation = 2.76
X = 200
Z= x μ
σ
Z=52.76
3.75 =0.597
P value corresponding to a Z-value of 0.597 for a two-tailed test at 0.05 level of significance is
0.5505

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