Question

The accompanying table contains data on the​ weight, in​ grams, of a sample of 50 tea bags produced during an​ eight-hour shift. Complete parts​ (a) through​ (d).

a. Is there evidence that the mean amount of tea per bag is different from 5.5 ​grams? (Use alphaαequals=0.10)

State the null and alternative hypotheses.

Upper H equals

5.55

Upper H ≠5.55

A). Determine the test statistic.

B). Find the p-value.

C). Construct a 90% confidence interval estimate of the population mean amount of tea per bag. Interpret this interval.

The 90% confidence interval is _ <= u <= _

Table:  

5.64
5.43
5.43
5.41
5.55
5.33
5.55
5.43
5.52
5.42
5.58
5.41
5.53
5.52
5.55
5.62
5.55
5.45
5.44
5.49
5.48
5.39
5.47
5.61
5.51
5.33
5.66
5.28
5.48
5.54
5.76
5.59
5.44
5.56
5.59
5.52
5.32
5.48
5.53
5.57
5.62
5.43
5.43
5.26
5.55
5.64
5.49
5.57
5.68
5.35

Answer 1

n=50,   = 5.55, = 0.10

Calculate mean and standard deviation for given data

We get,

= 5.4996, s= 0.105829

Ho: ​​​​​​​ = 5.55

Ha: ≠ 5.55

a)

Calculate the test statistic

t = -3.3675

test statistics =   -3.3675

b)

calculate the p-value using calculaor for two tailed test with

df= n-1 = 50-1 = 49

we get,

P-Value = 0.0015

c)

c= 90%

formula for confidenceinterval is

Where tc is the t critical value for c= 90% with df= n-1 = 50-1 =49

using t table we get

tc = 1.677

5.4745     5.5247

The 90% confidence interval is  5.4745     5.5247