Question

Please show step by step work in a spreadsheet or excel so I can follow along:

A federal agency responsible for enforcing laws governing weights and measures routinely inspects packages to determine whether the weight of the contents is at least as great as that advertised on the package. A random sample of 30 containers whose packaging states that the contents weigh 8 ounces was drawn. The weight of each package in ounces can be found in the sheet entitled “Part 2 Question 4”. After conducting the appropriate test, can you conclude with confidence that packages that are labeled as weighing 8 ounces are likely to weigh 8 ounces?

Package Weight in Ounces
7.80
7.91
7.93
7.99
7.94
7.75
7.97
7.95
7.79
8.06
7.82
7.89
7.92
7.87
7.92
7.98
8.05
7.91
7.88
7.95
8.03
8
7.76
7.88
7.99
7.79
8.01
7.8
8.05
8.05

Answer 1

Solution:-

State the hypotheses. The first step is to state the null hypothesis and an alternative hypothesis.

Null hypothesis: u = 8
Alternative hypothesis: u 8

Note that these hypotheses constitute a two-tailed test.

Formulate an analysis plan. For this analysis, the significance level is 0.05. The test method is a one-sample t-test.

Analyze sample data. Using sample data, we compute the standard error (SE), degrees of freedom (DF), and the t statistic test statistic (t).

SE = s / sqrt(n)

S.E = 0.01692

DF = n - 1

D.F = 29
t = (x - u) / SE

t = 4.65

where s is the standard deviation of the sample, x is the sample mean, u is the hypothesized population mean, and n is the sample size.

Since we have a two-tailed test, the P-value is the probability that the t statistic having 29 degrees of freedom is less than -4.65 or greater than 4.65.

Thus, the P-value = less than 0.001.

Interpret results. Since the P-value (almost 0) is less than the significance level (0.05), we have to reject the null hypothesis.