A Telecom service provider claims that individual customers pay on an average 400 rs. per monthwith standard deviation of 25 rs. A random sample of 50 customers’ bills during a given month istaken with a mean of 250 and standard deviation of 15. What to say with respect to the claim madeby the service provider?

The claim made by the service provider can be tested using a hypothesis test.

Step 1: State the Hypotheses The first step in hypothesis testing is to set the hypotheses. The null hypothesis states that the mean monthly bill is 400 rs. (the status quo), denoted by H0: μ = 400. The alternative hypothesis states that the mean monthly bill is not 400 rs., denoted by H1: μ ≠ 400.

Step 2: Formulate an Analysis Plan For this analysis, the significance level is defined as α = 0.05. The sample size is 50, which is large enough to use the z-distribution in the analysis.

Step 3: Analyze Sample Data Using sample data, we calculate the pooled sample mean (x̄) and the sample standard deviation (s). In this case, the sample mean (x̄) is 250 rs. and the sample standard deviation (s) is 15 rs.

Step 4: Interpret the Results We use the sample data to calculate the value of the test statistic. Under the null hypothesis, the test statistic follows a standard normal distribution.

z = (x̄ - μ) / (σ/√n) = (250 - 400) / (25/√50) = -150 / (25/√50) = -42.43

The critical value for a two-tailed test at the .05 significance level is approximately ± 1.96. Since -42.43 is less than -1.96, we reject the null hypothesis.

Therefore, we can say that the claim made by the service provider that individual customers pay on an average 400 rs. per month is not supported by the sample data.