It has been claimed from previous studies that the average diameter of ball bearings from this manufacturing process is 2.30 cm. Based on the sample of 50 that you collected, is there evidence to suggest that the average diameter is greater than 2.30 cm? Perform a hypothesis test for the population mean at alpha = 0.01. Define the null and alternative hypothesis for this test in mathematical terms and in words. Report the level of significance. Include the test statistic and the P-value. See Step 3 in the Python script. (Note that Python methods return two tailed P-values. You must report the correct P-value based on the alternative hypothesis.) Provide your conclusion and interpretation of the results. Should the null hypothesis be rejected? Why or why not? Diameters data frame diameters 0 2.69 1 1.64 2 1.85 3 2.21 4 3.30 5 3.27 6 2.77 7 2.07 8 2.61 9 2.74 10 2.19 11 2.62 12 2.04 13 3.10 14 2.62 15 3.05 16 2.36 17 2.18 18 2.31 19 2.69 20 2.43 21 2.31 22 2.39 23 3.38 24 3.62 25 1.42 26 2.08 27 2.62 28 2.09 29 1.52 30 2.81 31 2.09 32 2.63 33 3.56 34 2.79 35 2.26 36 3.33 37 2.48 38 3.03 39 2.45 40 3.21 41 2.31 42 3.20 43 2.90 44 2.30 45 3.21 46 2.11 47 1.53 48 3.15 49 2.73 90% confidence interval (unrounded) = (2.4486912846323325, 2.6813087153676674) 90% confidence interval (rounded) = ( 2.45 , 2.68 ) 99% confidence interval (unrounded) = (2.3828613632281552, 2.7471386367718447) 99% confidence interval (rounded) = ( 2.38 , 2.75 ) z-test hypothesis test for population mean test-statistic = 3.48 two tailed p-value = 0.0005
It has been claimed from previous studies that the average diameter of ball bearings from this manufacturing process is 2.30 cm. Based on the sample of 50 that you collected, is there evidence to suggest that the average diameter is greater than 2.30 cm? Perform a hypothesis test for the population mean at alpha = 0.01.
- Define the null and alternative hypothesis for this test in mathematical terms and in words.
- Report the level of significance.
- Include the test statistic and the P-value. See Step 3 in the Python script. (Note that Python methods return two tailed P-values. You must report the correct P-value based on the alternative hypothesis.)
- Provide your conclusion and interpretation of the results. Should the null hypothesis be rejected? Why or why not?
Diameters data frame
diameters
0 2.69
1 1.64
2 1.85
3 2.21
4 3.30
5 3.27
6 2.77
7 2.07
8 2.61
9 2.74
10 2.19
11 2.62
12 2.04
13 3.10
14 2.62
15 3.05
16 2.36
17 2.18
18 2.31
19 2.69
20 2.43
21 2.31
22 2.39
23 3.38
24 3.62
25 1.42
26 2.08
27 2.62
28 2.09
29 1.52
30 2.81
31 2.09
32 2.63
33 3.56
34 2.79
35 2.26
36 3.33
37 2.48
38 3.03
39 2.45
40 3.21
41 2.31
42 3.20
43 2.90
44 2.30
45 3.21
46 2.11
47 1.53
48 3.15
49 2.73
90% confidence interval (unrounded) = (2.4486912846323325, 2.6813087153676674)
90% confidence interval (rounded) = ( 2.45 , 2.68 )
99% confidence interval (unrounded) = (2.3828613632281552, 2.7471386367718447)
99% confidence interval (rounded) = ( 2.38 , 2.75 )
z-test hypothesis test for population mean
test-statistic = 3.48
two tailed p-value = 0.0005
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